table of integer factorizations for 0<n<1001

table of integer factorizations for

0

<

n

<

1001

In

addition

to the factorizations of the first

thousand

positive integers

, the following table also gives the values of the following functions:

Ω

⁢

(

n

)

, the number of (nondistinct)

prime factors

function;

ω

⁢

(

n

)

, the

number of distinct prime factors function

; the

difference

between the two

Ω

⁢

(

n

)

-

ω

⁢

(

n

)

(with the heading

Σ

a

for the sake of not making the table wider than necessary);

λ

⁢

(

n

)

, the

Liouville function

; and

μ

⁢

(

n

)

, the Möbius function.

n

Factorization

Ω

⁢

(

n

)

ω

⁢

(

n

)

Σ

a

λ

⁢

(

n

)

μ

⁢

(

n

)

1

Unit

0

0

0

1

1

2

Prime

1

1

0

-

1

-

1

3

Prime

1

1

0

-

1

-

1

4

2

2

2

1

1

1

0

5

Prime

1

1

0

-

1

-

1

6

2

⋅

3

2

2

0

1

1

7

Prime

1

1

0

-

1

-

1

8

2

3

3

1

2

-

1

0

9

3

2

2

1

1

1

0

10

2

⋅

5

2

2

0

1

1

11

Prime

1

1

0

-

1

-

1

12

2

2

⋅

3

3

2

1

-

1

0

13

Prime

1

1

0

-

1

-

1

14

2

⋅

7

2

2

0

1

1

15

3

⋅

5

2

2

0

1

1

16

2

4

4

1

3

1

0

17

Prime

1

1

0

-

1

-

1

18

2

⋅

3

2

3

2

1

-

1

0

19

Prime

1

1

0

-

1

-

1

20

2

2

⋅

5

3

2

1

-

1

0

21

3

⋅

7

2

2

0

1

1

22

2

⋅

11

2

2

0

1

1

23

Prime

1

1

0

-

1

-

1

24

2

3

⋅

3

4

2

2

1

0

25

5

2

2

1

1

1

0

26

2

⋅

13

2

2

0

1

1

27

3

3

3

1

2

-

1

0

28

2

2

⋅

7

3

2

1

-

1

0

29

Prime

1

1

0

-

1

-

1

30

2

⋅

3

⋅

5

3

3

0

-

1

-

1

31

Prime

1

1

0

-

1

-

1

32

2

5

5

1

4

-

1

0

33

3

⋅

11

2

2

0

1

1

34

2

⋅

17

2

2

0

1

1

35

5

⋅

7

2

2

0

1

1

36

2

2

⋅

3

2

4

2

2

1

0

37

Prime

1

1

0

-

1

-

1

38

2

⋅

19

2

2

0

1

1

39

3

⋅

13

2

2

0

1

1

40

2

3

⋅

5

4

2

2

1

0

41

Prime

1

1

0

-

1

-

1

42

2

⋅

3

⋅

7

3

3

0

-

1

-

1

43

Prime

1

1

0

-

1

-

1

44

2

2

⋅

11

3

2

1

-

1

0

45

3

2

⋅

5

3

2

1

-

1

0

46

2

⋅

23

2

2

0

1

1

47

Prime

1

1

0

-

1

-

1

48

2

4

⋅

3

5

2

3

-

1

0

49

7

2

2

1

1

1

0

50

2

⋅

5

2

3

2

1

-

1

0

51

3

⋅

17

2

2

0

1

1

52

2

2

⋅

13

3

2

1

-

1

0

53

Prime

1

1

0

-

1

-

1

54

2

⋅

3

3

4

2

2

1

0

55

5

⋅

11

2

2

0

1

1

56

2

3

⋅

7

4

2

2

1

0

57

3

⋅

19

2

2

0

1

1

58

2

⋅

29

2

2

0

1

1

59

Prime

1

1

0

-

1

-

1

60

2

2

⋅

3

⋅

5

4

3

1

1

0

61

Prime

1

1

0

-

1

-

1

62

2

⋅

31

2

2

0

1

1

63

3

2

⋅

7

3

2

1

-

1

0

64

2

6

6

1

5

1

0

65

5

⋅

13

2

2

0

1

1

66

2

⋅

3

⋅

11

3

3

0

-

1

-

1

67

Prime

1

1

0

-

1

-

1

68

2

2

⋅

17

3

2

1

-

1

0

69

3

⋅

23

2

2

0

1

1

70

2

⋅

5

⋅

7

3

3

0

-

1

-

1

71

Prime

1

1

0

-

1

-

1

72

2

3

⋅

3

2

5

2

3

-

1

0

73

Prime

1

1

0

-

1

-

1

74

2

⋅

37

2

2

0

1

1

75

3

⋅

5

2

3

2

1

-

1

0

76

2

2

⋅

19

3

2

1

-

1

0

77

7

⋅

11

2

2

0

1

1

78

2

⋅

3

⋅

13

3

3

0

-

1

-

1

79

Prime

1

1

0

-

1

-

1

80

2

4

⋅

5

5

2

3

-

1

0

81

3

4

4

1

3

1

0

82

2

⋅

41

2

2

0

1

1

83

Prime

1

1

0

-

1

-

1

84

2

2

⋅

3

⋅

7

4

3

1

1

0

85

5

⋅

17

2

2

0

1

1

86

2

⋅

43

2

2

0

1

1

87

3

⋅

29

2

2

0

1

1

88

2

3

⋅

11

4

2

2

1

0

89

Prime

1

1

0

-

1

-

1

90

2

⋅

3

2

⋅

5

4

3

1

1

0

91

7

⋅

13

2

2

0

1

1

92

2

2

⋅

23

3

2

1

-

1

0

93

3

⋅

31

2

2

0

1

1

94

2

⋅

47

2

2

0

1

1

95

5

⋅

19

2

2

0

1

1

96

2

5

⋅

3

6

2

4

1

0

97

Prime

1

1

0

-

1

-

1

98

2

⋅

7

2

3

2

1

-

1

0

99

3

2

⋅

11

3

2

1

-

1

0

100

2

2

⋅

5

2

4

2

2

1

0

101

Prime

1

1

0

-

1

-

1

102

2

⋅

3

⋅

17

3

3

0

-

1

-

1

103

Prime

1

1

0

-

1

-

1

104

2

3

⋅

13

4

2

2

1

0

105

3

⋅

5

⋅

7

3

3

0

-

1

-

1

106

2

⋅

53

2

2

0

1

1

107

Prime

1

1

0

-

1

-

1

108

2

2

⋅

3

3

5

2

3

-

1

0

109

Prime

1

1

0

-

1

-

1

110

2

⋅

5

⋅

11

3

3

0

-

1

-

1

111

3

⋅

37

2

2

0

1

1

112

2

4

⋅

7

5

2

3

-

1

0

113

Prime

1

1

0

-

1

-

1

114

2

⋅

3

⋅

19

3

3

0

-

1

-

1

115

5

⋅

23

2

2

0

1

1

116

2

2

⋅

29

3

2

1

-

1

0

117

3

2

⋅

13

3

2

1

-

1

0

118

2

⋅

59

2

2

0

1

1

119

7

⋅

17

2

2

0

1

1

120

2

3

⋅

3

⋅

5

5

3

2

-

1

0

121

11

2

2

1

1

1

0

122

2

⋅

61

2

2

0

1

1

123

3

⋅

41

2

2

0

1

1

124

2

2

⋅

31

3

2

1

-

1

0

125

5

3

3

1

2

-

1

0

126

2

⋅

3

2

⋅

7

4

3

1

1

0

127

Prime

1

1

0

-

1

-

1

128

2

7

7

1

6

-

1

0

129

3

⋅

43

2

2

0

1

1

130

2

⋅

5

⋅

13

3

3

0

-

1

-

1

131

Prime

1

1

0

-

1

-

1

132

2

2

⋅

3

⋅

11

4

3

1

1

0

133

7

⋅

19

2

2

0

1

1

134

2

⋅

67

2

2

0

1

1

135

3

3

⋅

5

4

2

2

1

0

136

2

3

⋅

17

4

2

2

1

0

137

Prime

1

1

0

-

1

-

1

138

2

⋅

3

⋅

23

3

3

0

-

1

-

1

139

Prime

1

1

0

-

1

-

1

140

2

2

⋅

5

⋅

7

4

3

1

1

0

141

3

⋅

47

2

2

0

1

1

142

2

⋅

71

2

2

0

1

1

143

11

⋅

13

2

2

0

1

1

144

2

4

⋅

3

2

6

2

4

1

0

145

5

⋅

29

2

2

0

1

1

146

2

⋅

73

2

2

0

1

1

147

3

⋅

7

2

3

2

1

-

1

0

148

2

2

⋅

37

3

2

1

-

1

0

149

Prime

1

1

0

-

1

-

1

150

2

⋅

3

⋅

5

2

4

3

1

1

0

151

Prime

1

1

0

-

1

-

1

152

2

3

⋅

19

4

2

2

1

0

153

3

2

⋅

17

3

2

1

-

1

0

154

2

⋅

7

⋅

11

3

3

0

-

1

-

1

155

5

⋅

31

2

2

0

1

1

156

2

2

⋅

3

⋅

13

4

3

1

1

0

157

Prime

1

1

0

-

1

-

1

158

2

⋅

79

2

2

0

1

1

159

3

⋅

53

2

2

0

1

1

160

2

5

⋅

5

6

2

4

1

0

161

7

⋅

23

2

2

0

1

1

162

2

⋅

3

4

5

2

3

-

1

0

163

Prime

1

1

0

-

1

-

1

164

2

2

⋅

41

3

2

1

-

1

0

165

3

⋅

5

⋅

11

3

3

0

-

1

-

1

166

2

⋅

83

2

2

0

1

1

167

Prime

1

1

0

-

1

-

1

168

2

3

⋅

3

⋅

7

5

3

2

-

1

0

169

13

2

2

1

1

1

0

170

2

⋅

5

⋅

17

3

3

0

-

1

-

1

171

3

2

⋅

19

3

2

1

-

1

0

172

2

2

⋅

43

3

2

1

-

1

0

173

Prime

1

1

0

-

1

-

1

174

2

⋅

3

⋅

29

3

3

0

-

1

-

1

175

5

2

⋅

7

3

2

1

-

1

0

176

2

4

⋅

11

5

2

3

-

1

0

177

3

⋅

59

2

2

0

1

1

178

2

⋅

89

2

2

0

1

1

179

Prime

1

1

0

-

1

-

1

180

2

2

⋅

3

2

⋅

5

5

3

2

-

1

0

181

Prime

1

1

0

-

1

-

1

182

2

⋅

7

⋅

13

3

3

0

-

1

-

1

183

3

⋅

61

2

2

0

1

1

184

2

3

⋅

23

4

2

2

1

0

185

5

⋅

37

2

2

0

1

1

186

2

⋅

3

⋅

31

3

3

0

-

1

-

1

187

11

⋅

17

2

2

0

1

1

188

2

2

⋅

47

3

2

1

-

1

0

189

3

3

⋅

7

4

2

2

1

0

190

2

⋅

5

⋅

19

3

3

0

-

1

-

1

191

Prime

1

1

0

-

1

-

1

192

2

6

⋅

3

7

2

5

-

1

0

193

Prime

1

1

0

-

1

-

1

194

2

⋅

97

2

2

0

1

1

195

3

⋅

5

⋅

13

3

3

0

-

1

-

1

196

2

2

⋅

7

2

4

2

2

1

0

197

Prime

1

1

0

-

1

-

1

198

2

⋅

3

2

⋅

11

4

3

1

1

0

199

Prime

1

1

0

-

1

-

1

200

2

3

⋅

5

2

5

2

3

-

1

0

201

3

⋅

67

2

2

0

1

1

202

2

⋅

101

2

2

0

1

1

203

7

⋅

29

2

2

0

1

1

204

2

2

⋅

3

⋅

17

4

3

1

1

0

205

5

⋅

41

2

2

0

1

1

206

2

⋅

103

2

2

0

1

1

207

3

2

⋅

23

3

2

1

-

1

0

208

2

4

⋅

13

5

2

3

-

1

0

209

11

⋅

19

2

2

0

1

1

210

2

⋅

3

⋅

5

⋅

7

4

4

0

1

1

211

Prime

1

1

0

-

1

-

1

212

2

2

⋅

53

3

2

1

-

1

0

213

3

⋅

71

2

2

0

1

1

214

2

⋅

107

2

2

0

1

1

215

5

⋅

43

2

2

0

1

1

216

2

3

⋅

3

3

6

2

4

1

0

217

7

⋅

31

2

2

0

1

1

218

2

⋅

109

2

2

0

1

1

219

3

⋅

73

2

2

0

1

1

220

2

2

⋅

5

⋅

11

4

3

1

1

0

221

13

⋅

17

2

2

0

1

1

222

2

⋅

3

⋅

37

3

3

0

-

1

-

1

223

Prime

1

1

0

-

1

-

1

224

2

5

⋅

7

6

2

4

1

0

225

3

2

⋅

5

2

4

2

2

1

0

226

2

⋅

113

2

2

0

1

1

227

Prime

1

1

0

-

1

-

1

228

2

2

⋅

3

⋅

19

4

3

1

1

0

229

Prime

1

1

0

-

1

-

1

230

2

⋅

5

⋅

23

3

3

0

-

1

-

1

231

3

⋅

7

⋅

11

3

3

0

-

1

-

1

232

2

3

⋅

29

4

2

2

1

0

233

Prime

1

1

0

-

1

-

1

234

2

⋅

3

2

⋅

13

4

3

1

1

0

235

5

⋅

47

2

2

0

1

1

236

2

2

⋅

59

3

2

1

-

1

0

237

3

⋅

79

2

2

0

1

1

238

2

⋅

7

⋅

17

3

3

0

-

1

-

1

239

Prime

1

1

0

-

1

-

1

240

2

4

⋅

3

⋅

5

6

3

3

1

0

241

Prime

1

1

0

-

1

-

1

242

2

⋅

11

2

3

2

1

-

1

0

243

3

5

5

1

4

-

1

0

244

2

2

⋅

61

3

2

1

-

1

0

245

5

⋅

7

2

3

2

1

-

1

0

246

2

⋅

3

⋅

41

3

3

0

-

1

-

1

247

13

⋅

19

2

2

0

1

1

248

2

3

⋅

31

4

2

2

1

0

249

3

⋅

83

2

2

0

1

1

250

2

⋅

5

3

4

2

2

1

0

251

Prime

1

1

0

-

1

-

1

252

2

2

⋅

3

2

⋅

7

5

3

2

-

1

0

253

11

⋅

23

2

2

0

1

1

254

2

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127

2

2

0

1

1

255

3

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5

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17

3

3

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1

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1

256

2

8

8

1

7

1

0

257

Prime

1

1

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1

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1

258

2

⋅

3

⋅

43

3

3

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1

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1

259

7

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37

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2

0

1

1

260

2

2

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5

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13

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3

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261

3

2

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29

3

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262

2

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131

2

2

0

1

1

263

Prime

1

1

0

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1

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1

264

2

3

⋅

3

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11

5

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265

5

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53

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2

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266

2

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7

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19

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267

3

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89

2

2

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1

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268

2

2

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67

3

2

1

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1

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269

Prime

1

1

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1

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270

2

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3

3

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5

5

3

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271

Prime

1

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1

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272

2

4

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273

3

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274

2

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11

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276

2

2

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3

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4

3

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277

Prime

1

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1

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1

278

2

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139

2

2

0

1

1

279

3

2

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31

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1

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1

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280

2

3

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5

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7

5

3

2

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1

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281

Prime

1

1

0

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1

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1

282

2

⋅

3

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47

3

3

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1

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1

283

Prime

1

1

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1

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1

284

2

2

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71

3

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1

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285

3

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286

2

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287

7

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288

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7

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289

17

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290

2

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29

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291

3

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97

2

2

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1

1

292

2

2

⋅

73

3

2

1

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1

0

293

Prime

1

1

0

-

1

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1

294

2

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3

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7

2

4

3

1

1

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295

5

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59

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2

0

1

1

296

2

3

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37

4

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297

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3

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11

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298

2

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149

2

2

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1

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299

13

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23

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300

2

2

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301

7

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302

2

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151

2

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303

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101

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304

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3

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305

5

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61

2

2

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306

2

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3

2

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17

4

3

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1

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307

Prime

1

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1

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1

308

2

2

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7

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11

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3

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1

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309

3

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103

2

2

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1

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310

2

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5

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31

3

3

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1

311

Prime

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312

2

3

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3

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313

Prime

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1

314

2

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157

2

2

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1

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315

3

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7

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3

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316

2

2

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79

3

2

1

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1

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317

Prime

1

1

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1

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1

318

2

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3

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53

3

3

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1

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1

319

11

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320

2

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321

3

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107

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322

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7

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323

17

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324

2

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325

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326

2

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163

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327

3

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109

2

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328

2

3

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41

4

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329

7

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47

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2

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330

2

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331

Prime

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1

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332

2

2

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83

3

2

1

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333

3

2

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37

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334

2

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167

2

2

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5

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67

2

2

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1

1

336

2

4

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3

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7

6

3

3

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337

Prime

1

1

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1

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1

338

2

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13

2

3

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1

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339

3

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113

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340

2

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11

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7

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345

3

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5

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23

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1

346

2

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173

2

2

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1

1

347

Prime

1

1

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1

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1

348

2

2

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3

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29

4

3

1

1

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349

Prime

1

1

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1

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1

350

2

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5

2

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7

4

3

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351

3

3

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13

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352

2

5

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11

6

2

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1

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353

Prime

1

1

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1

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1

354

2

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3

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59

3

3

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1

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1

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5

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356

2

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357

3

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7

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17

3

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358

2

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179

2

2

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359

Prime

1

1

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1

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1

360

2

3

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3

2

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5

6

3

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1

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19

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362

2

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181

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363

3

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5

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73

2

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1

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366

2

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3

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61

3

3

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1

367

Prime

1

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1

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1

368

2

4

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23

5

2

3

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1

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369

3

2

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41

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1

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370

2

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37

3

3

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7

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53

2

2

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2

2

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3

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31

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3

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373

Prime

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1

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2

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3

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3

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4

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376

2

3

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47

4

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377

13

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29

2

2

0

1

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378

2

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3

3

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7

5

3

2

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1

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379

Prime

1

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1

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1

380

2

2

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5

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19

4

3

1

1

0

381

3

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127

2

2

0

1

1

382

2

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191

2

2

0

1

1

383

Prime

1

1

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1

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1

384

2

7

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3

8

2

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1

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385

5

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7

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3

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386

2

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193

2

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387

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43

3

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388

2

2

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97

3

2

1

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1

0

389

Prime

1

1

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1

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1

390

2

⋅

3

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5

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13

4

4

0

1

1

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17

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23

2

2

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1

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392

2

3

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7

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5

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3

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393

3

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131

2

2

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1

394

2

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197

2

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1

395

5

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79

2

2

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1

1

396

2

2

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3

2

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11

5

3

2

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1

0

397

Prime

1

1

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-

1

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1

398

2

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199

2

2

0

1

1

399

3

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7

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19

3

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400

2

4

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5

2

6

2

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1

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401

Prime

1

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1

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1

402

2

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3

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67

3

3

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13

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2

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101

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405

3

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5

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2

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11

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2

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2

3

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3

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17

5

3

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409

Prime

1

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1

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2

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41

3

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411

3

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137

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2

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103

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7

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59

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2

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5

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3

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139

2

2

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2

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11

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19

3

3

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419

Prime

1

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1

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2

2

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3

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5

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7

5

4

1

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421

Prime

1

1

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1

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422

2

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211

2

2

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1

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3

2

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47

3

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424

2

3

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5

2

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2

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7

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2

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107

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3

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2

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43

3

3

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431

Prime

1

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1

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432

2

4

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3

3

7

2

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433

Prime

1

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1

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434

2

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7

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31

3

3

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3

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2

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19

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2

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3

3

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Prime

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2

3

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5

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3

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7

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2

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3

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Prime

1

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2

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5

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2

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2

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2

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3

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149

2

2

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2

6

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7

7

2

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1

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449

Prime

1

1

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1

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450

2

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3

2

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5

2

5

3

2

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1

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11

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41

2

2

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2

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113

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3

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151

2

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454

2

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227

2

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5

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7

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2

3

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3

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19

5

3

2

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1

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457

Prime

1

1

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1

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1

458

2

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229

2

2

0

1

1

459

3

3

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17

4

2

2

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460

2

2

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5

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23

4

3

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461

Prime

1

1

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1

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1

462

2

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3

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7

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11

4

4

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1

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463

Prime

1

1

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1

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1

464

2

4

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29

5

2

3

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1

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465

3

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31

3

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2

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2

2

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Prime

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2

2

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3

2

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7

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470

2

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3

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2

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2

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11

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2

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3

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476

2

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7

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3

2

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53

3

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1

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1

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478

2

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239

2

2

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1

1

479

Prime

1

1

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1

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1

480

2

5

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3

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5

7

3

4

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1

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481

13

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37

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2

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2

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241

2

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3

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7

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2

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485

5

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97

2

2

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2

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3

5

6

2

4

1

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487

Prime

1

1

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1

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1

488

2

3

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61

4

2

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1

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489

3

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163

2

2

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1

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490

2

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5

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7

2

4

3

1

1

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491

Prime

1

1

0

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1

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1

492

2

2

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3

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41

4

3

1

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493

17

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29

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2

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13

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3

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2

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7

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2

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3

3

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Prime

1

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2

2

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5

3

5

2

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3

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167

2

2

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1

1

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2

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251

2

2

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1

503

Prime

1

1

0

-

1

-

1

504

2

3

⋅

3

2

⋅

7

6

3

3

1

0

505

5

⋅

101

2

2

0

1

1

506

2

⋅

11

⋅

23

3

3

0

-

1

-

1

507

3

⋅

13

2

3

2

1

-

1

0

508

2

2

⋅

127

3

2

1

-

1

0

509

Prime

1

1

0

-

1

-

1

510

2

⋅

3

⋅

5

⋅

17

4

4

0

1

1

511

7

⋅

73

2

2

0

1

1

512

2

9

9

1

8

-

1

0

513

3

3

⋅

19

4

2

2

1

0

514

2

⋅

257

2

2

0

1

1

515

5

⋅

103

2

2

0

1

1

516

2

2

⋅

3

⋅

43

4

3

1

1

0

517

11

⋅

47

2

2

0

1

1

518

2

⋅

7

⋅

37

3

3

0

-

1

-

1

519

3

⋅

173

2

2

0

1

1

520

2

3

⋅

5

⋅

13

5

3

2

-

1

0

521

Prime

1

1

0

-

1

-

1

522

2

⋅

3

2

⋅

29

4

3

1

1

0

523

Prime

1

1

0

-

1

-

1

524

2

2

⋅

131

3

2

1

-

1

0

525

3

⋅

5

2

⋅

7

4

3

1

1

0

526

2

⋅

263

2

2

0

1

1

527

17

⋅

31

2

2

0

1

1

528

2

4

⋅

3

⋅

11

6

3

3

1

0

529

23

2

2

1

1

1

0

530

2

⋅

5

⋅

53

3

3

0

-

1

-

1

531

3

2

⋅

59

3

2

1

-

1

0

532

2

2

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7

⋅

19

4

3

1

1

0

533

13

⋅

41

2

2

0

1

1

534

2

⋅

3

⋅

89

3

3

0

-

1

-

1

535

5

⋅

107

2

2

0

1

1

536

2

3

⋅

67

4

2

2

1

0

537

3

⋅

179

2

2

0

1

1

538

2

⋅

269

2

2

0

1

1

539

7

2

⋅

11

3

2

1

-

1

0

540

2

2

⋅

3

3

⋅

5

6

3

3

1

0

541

Prime

1

1

0

-

1

-

1

542

2

⋅

271

2

2

0

1

1

543

3

⋅

181

2

2

0

1

1

544

2

5

⋅

17

6

2

4

1

0

545

5

⋅

109

2

2

0

1

1

546

2

⋅

3

⋅

7

⋅

13

4

4

0

1

1

547

Prime

1

1

0

-

1

-

1

548

2

2

⋅

137

3

2

1

-

1

0

549

3

2

⋅

61

3

2

1

-

1

0

550

2

⋅

5

2

⋅

11

4

3

1

1

0

551

19

⋅

29

2

2

0

1

1

552

2

3

⋅

3

⋅

23

5

3

2

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1

0

553

7

⋅

79

2

2

0

1

1

554

2

⋅

277

2

2

0

1

1

555

3

⋅

5

⋅

37

3

3

0

-

1

-

1

556

2

2

⋅

139

3

2

1

-

1

0

557

Prime

1

1

0

-

1

-

1

558

2

⋅

3

2

⋅

31

4

3

1

1

0

559

13

⋅

43

2

2

0

1

1

560

2

4

⋅

5

⋅

7

6

3

3

1

0

561

3

⋅

11

⋅

17

3

3

0

-

1

-

1

562

2

⋅

281

2

2

0

1

1

563

Prime

1

1

0

-

1

-

1

564

2

2

⋅

3

⋅

47

4

3

1

1

0

565

5

⋅

113

2

2

0

1

1

566

2

⋅

283

2

2

0

1

1

567

3

4

⋅

7

5

2

3

-

1

0

568

2

3

⋅

71

4

2

2

1

0

569

Prime

1

1

0

-

1

-

1

570

2

⋅

3

⋅

5

⋅

19

4

4

0

1

1

571

Prime

1

1

0

-

1

-

1

572

2

2

⋅

11

⋅

13

4

3

1

1

0

573

3

⋅

191

2

2

0

1

1

574

2

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7

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41

3

3

0

-

1

-

1

575

5

2

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23

3

2

1

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1

0

576

2

6

⋅

3

2

8

2

6

1

0

577

Prime

1

1

0

-

1

-

1

578

2

⋅

17

2

3

2

1

-

1

0

579

3

⋅

193

2

2

0

1

1

580

2

2

⋅

5

⋅

29

4

3

1

1

0

581

7

⋅

83

2

2

0

1

1

582

2

⋅

3

⋅

97

3

3

0

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1

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1

583

11

⋅

53

2

2

0

1

1

584

2

3

⋅

73

4

2

2

1

0

585

3

2

⋅

5

⋅

13

4

3

1

1

0

586

2

⋅

293

2

2

0

1

1

587

Prime

1

1

0

-

1

-

1

588

2

2

⋅

3

⋅

7

2

5

3

2

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1

0

589

19

⋅

31

2

2

0

1

1

590

2

⋅

5

⋅

59

3

3

0

-

1

-

1

591

3

⋅

197

2

2

0

1

1

592

2

4

⋅

37

5

2

3

-

1

0

593

Prime

1

1

0

-

1

-

1

594

2

⋅

3

3

⋅

11

5

3

2

-

1

0

595

5

⋅

7

⋅

17

3

3

0

-

1

-

1

596

2

2

⋅

149

3

2

1

-

1

0

597

3

⋅

199

2

2

0

1

1

598

2

⋅

13

⋅

23

3

3

0

-

1

-

1

599

Prime

1

1

0

-

1

-

1

600

2

3

⋅

3

⋅

5

2

6

3

3

1

0

601

Prime

1

1

0

-

1

-

1

602

2

⋅

7

⋅

43

3

3

0

-

1

-

1

603

3

2

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67

3

2

1

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1

0

604

2

2

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151

3

2

1

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1

0

605

5

⋅

11

2

3

2

1

-

1

0

606

2

⋅

3

⋅

101

3

3

0

-

1

-

1

607

Prime

1

1

0

-

1

-

1

608

2

5

⋅

19

6

2

4

1

0

609

3

⋅

7

⋅

29

3

3

0

-

1

-

1

610

2

⋅

5

⋅

61

3

3

0

-

1

-

1

611

13

⋅

47

2

2

0

1

1

612

2

2

⋅

3

2

⋅

17

5

3

2

-

1

0

613

Prime

1

1

0

-

1

-

1

614

2

⋅

307

2

2

0

1

1

615

3

⋅

5

⋅

41

3

3

0

-

1

-

1

616

2

3

⋅

7

⋅

11

5

3

2

-

1

0

617

Prime

1

1

0

-

1

-

1

618

2

⋅

3

⋅

103

3

3

0

-

1

-

1

619

Prime

1

1

0

-

1

-

1

620

2

2

⋅

5

⋅

31

4

3

1

1

0

621

3

3

⋅

23

4

2

2

1

0

622

2

⋅

311

2

2

0

1

1

623

7

⋅

89

2

2

0

1

1

624

2

4

⋅

3

⋅

13

6

3

3

1

0

625

5

4

4

1

3

1

0

626

2

⋅

313

2

2

0

1

1

627

3

⋅

11

⋅

19

3

3

0

-

1

-

1

628

2

2

⋅

157

3

2

1

-

1

0

629

17

⋅

37

2

2

0

1

1

630

2

⋅

3

2

⋅

5

⋅

7

5

4

1

-

1

0

631

Prime

1

1

0

-

1

-

1

632

2

3

⋅

79

4

2

2

1

0

633

3

⋅

211

2

2

0

1

1

634

2

⋅

317

2

2

0

1

1

635

5

⋅

127

2

2

0

1

1

636

2

2

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3

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53

4

3

1

1

0

637

7

2

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13

3

2

1

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1

0

638

2

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11

⋅

29

3

3

0

-

1

-

1

639

3

2

⋅

71

3

2

1

-

1

0

640

2

7

⋅

5

8

2

6

1

0

641

Prime

1

1

0

-

1

-

1

642

2

⋅

3

⋅

107

3

3

0

-

1

-

1

643

Prime

1

1

0

-

1

-

1

644

2

2

⋅

7

⋅

23

4

3

1

1

0

645

3

⋅

5

⋅

43

3

3

0

-

1

-

1

646

2

⋅

17

⋅

19

3

3

0

-

1

-

1

647

Prime

1

1

0

-

1

-

1

648

2

3

⋅

3

4

7

2

5

-

1

0

649

11

⋅

59

2

2

0

1

1

650

2

⋅

5

2

⋅

13

4

3

1

1

0

651

3

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7

⋅

31

3

3

0

-

1

-

1

652

2

2

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163

3

2

1

-

1

0

653

Prime

1

1

0

-

1

-

1

654

2

⋅

3

⋅

109

3

3

0

-

1

-

1

655

5

⋅

131

2

2

0

1

1

656

2

4

⋅

41

5

2

3

-

1

0

657

3

2

⋅

73

3

2

1

-

1

0

658

2

⋅

7

⋅

47

3

3

0

-

1

-

1

659

Prime

1

1

0

-

1

-

1

660

2

2

⋅

3

⋅

5

⋅

11

5

4

1

-

1

0

661

Prime

1

1

0

-

1

-

1

662

2

⋅

331

2

2

0

1

1

663

3

⋅

13

⋅

17

3

3

0

-

1

-

1

664

2

3

⋅

83

4

2

2

1

0

665

5

⋅

7

⋅

19

3

3

0

-

1

-

1

666

2

⋅

3

2

⋅

37

4

3

1

1

0

667

23

⋅

29

2

2

0

1

1

668

2

2

⋅

167

3

2

1

-

1

0

669

3

⋅

223

2

2

0

1

1

670

2

⋅

5

⋅

67

3

3

0

-

1

-

1

671

11

⋅

61

2

2

0

1

1

672

2

5

⋅

3

⋅

7

7

3

4

-

1

0

673

Prime

1

1

0

-

1

-

1

674

2

⋅

337

2

2

0

1

1

675

3

3

⋅

5

2

5

2

3

-

1

0

676

2

2

⋅

13

2

4

2

2

1

0

677

Prime

1

1

0

-

1

-

1

678

2

⋅

3

⋅

113

3

3

0

-

1

-

1

679

7

⋅

97

2

2

0

1

1

680

2

3

⋅

5

⋅

17

5

3

2

-

1

0

681

3

⋅

227

2

2

0

1

1

682

2

⋅

11

⋅

31

3

3

0

-

1

-

1

683

Prime

1

1

0

-

1

-

1

684

2

2

⋅

3

2

⋅

19

5

3

2

-

1

0

685

5

⋅

137

2

2

0

1

1

686

2

⋅

7

3

4

2

2

1

0

687

3

⋅

229

2

2

0

1

1

688

2

4

⋅

43

5

2

3

-

1

0

689

13

⋅

53

2

2

0

1

1

690

2

⋅

3

⋅

5

⋅

23

4

4

0

1

1

691

Prime

1

1

0

-

1

-

1

692

2

2

⋅

173

3

2

1

-

1

0

693

3

2

⋅

7

⋅

11

4

3

1

1

0

694

2

⋅

347

2

2

0

1

1

695

5

⋅

139

2

2

0

1

1

696

2

3

⋅

3

⋅

29

5

3

2

-

1

0

697

17

⋅

41

2

2

0

1

1

698

2

⋅

349

2

2

0

1

1

699

3

⋅

233

2

2

0

1

1

700

2

2

⋅

5

2

⋅

7

5

3

2

-

1

0

701

Prime

1

1

0

-

1

-

1

702

2

⋅

3

3

⋅

13

5

3

2

-

1

0

703

19

⋅

37

2

2

0

1

1

704

2

6

⋅

11

7

2

5

-

1

0

705

3

⋅

5

⋅

47

3

3

0

-

1

-

1

706

2

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353

2

2

0

1

1

707

7

⋅

101

2

2

0

1

1

708

2

2

⋅

3

⋅

59

4

3

1

1

0

709

Prime

1

1

0

-

1

-

1

710

2

⋅

5

⋅

71

3

3

0

-

1

-

1

711

3

2

⋅

79

3

2

1

-

1

0

712

2

3

⋅

89

4

2

2

1

0

713

23

⋅

31

2

2

0

1

1

714

2

⋅

3

⋅

7

⋅

17

4

4

0

1

1

715

5

⋅

11

⋅

13

3

3

0

-

1

-

1

716

2

2

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179

3

2

1

-

1

0

717

3

⋅

239

2

2

0

1

1

718

2

⋅

359

2

2

0

1

1

719

Prime

1

1

0

-

1

-

1

720

2

4

⋅

3

2

⋅

5

7

3

4

-

1

0

721

7

⋅

103

2

2

0

1

1

722

2

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19

2

3

2

1

-

1

0

723

3

⋅

241

2

2

0

1

1

724

2

2

⋅

181

3

2

1

-

1

0

725

5

2

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29

3

2

1

-

1

0

726

2

⋅

3

⋅

11

2

4

3

1

1

0

727

Prime

1

1

0

-

1

-

1

728

2

3

⋅

7

⋅

13

5

3

2

-

1

0

729

3

6

6

1

5

1

0

730

2

⋅

5

⋅

73

3

3

0

-

1

-

1

731

17

⋅

43

2

2

0

1

1

732

2

2

⋅

3

⋅

61

4

3

1

1

0

733

Prime

1

1

0

-

1

-

1

734

2

⋅

367

2

2

0

1

1

735

3

⋅

5

⋅

7

2

4

3

1

1

0

736

2

5

⋅

23

6

2

4

1

0

737

11

⋅

67

2

2

0

1

1

738

2

⋅

3

2

⋅

41

4

3

1

1

0

739

Prime

1

1

0

-

1

-

1

740

2

2

⋅

5

⋅

37

4

3

1

1

0

741

3

⋅

13

⋅

19

3

3

0

-

1

-

1

742

2

⋅

7

⋅

53

3

3

0

-

1

-

1

743

Prime

1

1

0

-

1

-

1

744

2

3

⋅

3

⋅

31

5

3

2

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1

0

745

5

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149

2

2

0

1

1

746

2

⋅

373

2

2

0

1

1

747

3

2

⋅

83

3

2

1

-

1

0

748

2

2

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7

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2

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3

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Prime

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3

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2

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2

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2

2

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3

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Prime

1

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2

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2

2

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3

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Prime

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2

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2

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13

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2

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2

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769

Prime

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2

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7

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3

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2

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2

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Prime

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2

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2

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2

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2

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2

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19

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3

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Prime

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2

2

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197

3

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3

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7

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Prime

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2

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2

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4

2

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Prime

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2

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4

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6

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3

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Prime

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2

2

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7

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3

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2

2

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Prime

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2

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3

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Prime

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2

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Prime

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2

2

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2

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Prime

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2

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3

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2

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Prime

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2

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7

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2

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2

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3

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2

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2

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2

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23

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37

2

2

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2

2

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3

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4

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Prime

1

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2

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7

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3

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2

3

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4

2

2

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Prime

1

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2

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3

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11

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4

4

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Prime

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2

2

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3

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3

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7

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3

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2

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2

2

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Prime

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864

2

5

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3

3

8

2

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5

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11

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2

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2

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13

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7

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2

2

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3

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73

4

3

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877

Prime

1

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1

-

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878

2

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439

2

2

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1

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3

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293

2

2

0

1

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880

2

4

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5

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11

6

3

3

1

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Prime

1

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1

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2

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3

2

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7

2

5

3

2

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Prime

1

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2

2

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13

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4

3

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3

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3

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2

2

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Prime

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2

3

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3

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5

3

2

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7

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2

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2

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3

3

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3

4

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2

2

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3

2

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19

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2

2

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2

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3

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3

3

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5

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2

2

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2

7

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7

8

2

6

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3

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13

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3

3

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2

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2

2

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29

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31

2

2

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2

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2

6

3

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17

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53

2

2

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2

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11

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41

3

3

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3

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3

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2

3

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113

4

2

2

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5

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181

2

2

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1

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2

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3

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3

3

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Prime

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1

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2

2

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227

3

2

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3

2

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3

2

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910

2

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5

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7

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4

4

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Prime

1

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912

2

4

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3

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19

6

3

3

1

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913

11

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2

2

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2

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2

2

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3

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3

3

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2

2

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3

2

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1

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917

7

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2

2

0

1

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2

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3

3

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17

5

3

2

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1

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919

Prime

1

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920

2

3

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5

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23

5

3

2

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1

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921

3

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307

2

2

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1

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2

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2

2

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13

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2

2

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2

2

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3

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7

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5

4

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5

2

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37

3

2

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2

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2

2

0

1

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3

2

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103

3

2

1

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1

0

928

2

5

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29

6

2

4

1

0

929

Prime

1

1

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1

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2

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3

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5

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31

4

4

0

1

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7

2

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19

3

2

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2

2

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233

3

2

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3

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311

2

2

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2

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2

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5

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3

3

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1

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2

3

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3

2

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6

3

3

1

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Prime

1

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938

2

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7

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67

3

3

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3

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313

2

2

0

1

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940

2

2

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5

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47

4

3

1

1

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941

Prime

1

1

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1

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942

2

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3

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157

3

3

0

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1

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23

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41

2

2

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2

4

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5

2

3

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3

3

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5

3

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2

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11

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43

3

3

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947

Prime

1

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1

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948

2

2

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3

⋅

79

4

3

1

1

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949

13

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2

2

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1

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2

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2

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19

4

3

1

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3

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317

2

2

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2

3

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7

⋅

17

5

3

2

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1

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Prime

1

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1

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2

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3

2

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53

4

3

1

1

0

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5

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2

2

0

1

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2

2

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239

3

2

1

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1

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3

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11

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29

3

3

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2

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2

2

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7

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2

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2

6

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8

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5

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31

2

2

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2

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3

3

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3

2

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3

2

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2

2

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3

2

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5

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2

2

0

1

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966

2

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3

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7

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4

4

0

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Prime

1

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1

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1

968

2

3

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11

2

5

2

3

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1

0

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3

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17

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19

3

3

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2

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5

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97

3

3

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971

Prime

1

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0

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1

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1

972

2

2

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3

5

7

2

5

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1

0

973

7

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2

2

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2

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2

2

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3

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2

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13

4

3

1

1

0

976

2

4

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5

2

3

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1

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977

Prime

1

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1

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2

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3

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163

3

3

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1

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11

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2

2

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2

2

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2

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3

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3

2

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109

3

2

1

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1

0

982

2

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491

2

2

0

1

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983

Prime

1

1

0

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1

-

1

984

2

3

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3

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41

5

3

2

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1

0

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5

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2

2

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2

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17

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29

3

3

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3

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7

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3

3

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2

2

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19

4

3

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23

⋅

43

2

2

0

1

1

990

2

⋅

3

2

⋅

5

⋅

11

5

4

1

-

1

0

991

Prime

1

1

0

-

1

-

1

992

2

5

⋅

31

6

2

4

1

0

993

3

⋅

331

2

2

0

1

1

994

2

⋅

7

⋅

71

3

3

0

-

1

-

1

995

5

⋅

199

2

2

0

1

1

996

2

2

⋅

3

⋅

83

4

3

1

1

0

997

Prime

1

1

0

-

1

-

1

998

2

⋅

499

2

2

0

1

1

999

3

3

⋅

37

4

2

2

1

0

1000

2

3

⋅

5

3

6

2

4

1

0

Title

table of

integer factorizations

for

0

<

n

<

1001

Canonical

name

TableOfIntegerFactorizationsFor0N1001

Date of creation

2013-03-22 17:54:58

Last modified on

2013-03-22 17:54:58

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Data Structure

Classification

msc 11A41

Generated on Fri Feb 9 15:18:38 2018 by

LaTeXML