nyuuzyou/wikis huggingface dataset:
35,925,119

== Number ==
$35 \, 925 \, 119$ (thirty-five million, nine hundred and twenty-five thousand, one hundred and nineteen) is:
:The $2 \, 199 \, 933$rd prime number
:The $6$th term of the smallest Cunningham chain of the first kind of length $7$:
::$1 \, 122 \, 659$, $2 \, 245 \, 319$, $4 \, 490 \, 639$, $8 \, 981 \, 279$, $17 \, 962 \, 559$, $35 \, 925 \, 119$, $71 \, 850 \, 239$
== Also see ==
* 
* 
Category:Specific Numbers
Category:35,925,119
350

== Number ==
$350$ (three hundred and fifty) is:
:$2 \times 5^2 \times 7$
:The $8$th primitive semiperfect number after $6, 20, 28, 88, 104, 272, 304$:
::$350 = 1 + 5 + 14 + 35 + 50 + 70 + 175$
:The $18$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$, $125$, $130$, $190$, $205$, $223$, $253$, $285$, $305$ the decimal representation of whose square can be split into two parts which are each themselves square:
::$350^2 = 122 \, 500$; $1 = 1^2$, $22 \, 500 = 150^2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:350
3507

== Number ==
$3507$ (three thousand, five hundred and seven) is:
:$3 \times 7 \times 167$
:The $19$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$, $469$, $546$, $974$, $1963$, $3507$
== Also see ==
* 
Category:Specific Numbers
Category:3507
351

== Number ==
$351$ (three hundred and fifty-one) is:
:$3^3 \times 13$
:The $3$rd triangular number after $28$, $91$ which is the sum of $2$ cubes:
::$351 = 125 + 216 = 5^3 + 6^3$
:The $26$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $171$, $190$, $210$, $231$, $253$, $276$, $300$, $325$:
::$351 = \ds \sum_{k \mathop = 1}^{26} k = \dfrac {26 \times \paren {26 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:351
351,120

== Number ==
$351 \, 120$ (three hundred and fifty-one thousand, one hundred and twenty) is:
:$2^4 \times 3 \times 5 \times 7 \times 11 \times 19$
:Can be represented as the sum of $3$, $4$, $5$, $6$, $7$ or $8$ cubes:
== Also see ==
* Cube which can be Represented as Sum of 3, 4, 5, 6, 7 or 8 Cubes
== Sources ==
* : $351,120$
* : $351,120$
Category:Specific Numbers
Category:351,120
3511

== Number ==
$3511$ (three thousand, five hundred and eleven) is:
:The $490$th prime number
:The $2$nd of the only $2$ known Wieferich primes, after $1093$:
::$3511^2 \divides 2^{3510} - 1$
== Also see ==
* 
* 
== Sources ==
* 
* : $3511$
* : $3511$
Category:Specific Numbers
Category:3511
352

== Number ==
$352$ (three hundred and fifty-two) is:
:$2^5 \times 11$
:The $15$th positive integer after $64$, $96$, $128$, $144$, $160$, $192$, $216$, $224$, $240$, $256$, $288$, $320$, $324$, $336$ with $6$ or more prime factors:
::$352 = 2 \times 2 \times 2 \times 2 \times 2 \times 11$
:The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $20$ different ways
== Also see ==
* 
* 
Category:Specific Numbers
Category:352
353

== Number ==
$353$ (three hundred and fifty-three) is:
:The $71$st prime number
:The $1$st positive integer such that its fourth power is the sum of $4$ other fourth powers of positive integers with no common factors:
::$353^4 = 30^4 + 120^4 + 272^4 + 315^4$
:The $11$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$, $113$, $193$, $241$, $257$:
::$353 = 11 \times 2^5 + 1$
:The $12$th palindromic prime:
::$2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $191$, $313$, $353$, $\ldots$
:The $18$th near-repdigit prime after $101$, $113$, $131$, $151$, $181$, $191$, $199$, $211$, $223$, $227$, $229$, $233$, $277$, $311$, $313$, $331$, $337$
:The $27$th left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $197$, $223$, $283$, $313$, $317$, $337$, $347$
== Also see ==
* 
* 
* 
* 
* 
* 
== Sources ==
* : $353$
* : $353$
Category:Specific Numbers
Category:353
354

== Number ==
$354$ (three hundred and fifty-four) is:
:$2 \times 3 \times 59$
:The $37$th sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $246$, $255$, $258$, $266$, $273$, $282$, $285$, $286$, $290$, $310$, $318$, $322$, $354$:
::$354 = 2 \times 3 \times 59$
== Also see ==
* 
Category:Specific Numbers
Category:354
355

== Number ==
$355$ (three hundred and fifty-five) is:
:$5 \times 71$
:The $14$th Smith number after $4$, $22$, $27$, $58$, $85$, $94$, $121$, $166$, $202$, $265$, $274$, $319$, $346$:
::$3 + 5 + 5 = 5 + 7 + 1 = 13$
== Also see ==
* 
Category:Specific Numbers
Category:355
3553

== Number ==
$3553$ (three thousand, five hundred and fifty-three) is:
:$11 \times 17 \times 19$
:The $38$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $\ldots$, $2205$, $2356$, $2512$, $2673$, $2839$, $3010$, $3186$, $3367$:
::$3553 = \ds \sum_{k \mathop = 1}^{38} \paren {5 k - 4} = \dfrac {38 \paren {5 \times 38 - 3} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:3553
357

== Number ==
$357$ (three hundred and fifty-seven) is:
:$3 \times 7 \times 17$
:The $16$th integer $n$ after $1$, $3$, $15$, $30$, $35$, $56$, $70$, $78$, $105$, $140$, $168$, $190$, $210$, $248$, $264$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
::$\map {\sigma_0} {357} = 8$, $\map \phi {357} = 192$, $\map {\sigma_1} {357} = 576$
:The $20$th number after $1$, $3$, $22$, $66$, $70$, $81$, $94$, $115$, $119$, $170$, $210$, $214$, $217$, $265$, $282$, $310$, $322$, $343$, $345$ whose divisor sum is square:
:
:The $38$th sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$:
::$357 = 3 \times 7 \times 17$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:357
357,686,312,646,216,567,629,137

== Number ==
$357 \, 686 \, 312 \, 646 \, 216 \, 567 \, 629 \, 137$ is:
:A prime number
:The largest left-truncatable prime
== Also see ==
* 
* 
== Sources ==
* : $357,686,312,646,216,567,629,137$
* : $357,686,312,646,216,567,629,137$
Category:Specific Numbers
Category:357,686,312,646,216,567,629,137
3570

== Number ==
$3570$ (three thousand, five hundred and seventy) is:
:$2 \times 3 \times 5 \times 7 \times 17$
:The $84$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $2701$, $2775$, $2850$, $2926$, $3003$, $3081$, $3160$, $3240$, $3321$, $3403$, $3486$:
::$3570 = \ds \sum_{k \mathop = 1}^{84} k = \dfrac {84 \times \paren {84 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:3570
3571

== Number ==
$3571$ (three thousand, five hundred and seventy-one) is:
:The $500$th prime number
:The $10$th Lucas prime after $2$, $3$, $7$, $11$, $29$, $47$, $199$, $521$, $2207$.
:The $17$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$, $29$, $47$, $76$, $123$, $199$, $322$, $521$, $843$, $1364$, $2207$:
::$3571 = 1364 + 2207$
:The $35$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $\ldots$, $2791$, $2977$, $3169$, $3367$:
::$3571 = \ds 1 + \sum_{k \mathop = 1}^{35 - 1} 6 k = 35^3 - 34^3$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:3571
358,336

== Number ==
$358 \, 336$ (three hundred and fifty-eight thousand, three hundred and thirty-six) is:
:$2^6 \times 11 \times 509$
:The $11$th term of a sociable chain of order $28$ whose smallest term is $14 \, 316$:
::$14 \, 316$, $19 \, 116$, $31 \, 704$, $47 \, 616$, $83 \, 328$, $177 \, 792$, $295 \, 488$, $629 \, 072$, $589 \, 786$, $294 \, 896$, $358 \, 336$, $418 \, 904$, $366 \, 556$, $274 \, 924$, $275 \, 444$, $243 \, 760$, $376 \, 736$, $381 \, 028$, $285 \, 778$, $152\, 990$, $122 \, 410$, $97 \, 946$, $48 \, 976$, $45 \, 946$, $22 \, 976$, $22 \, 744$, $19 \, 916$, $17 \, 716$, $14 \, 316$, $\ldots$
== Also see ==
* 
Category:Specific Numbers
Category:358,336
359

== Number ==
$359$ (three hundred and fifty-nine) is:
:The $72$nd prime number
:The smaller of the $2$nd pair of primes whose prime gap is $8$:
::$367 - 359 = 8$
:The $3$rd term after $89, 179$ of the smallest Cunningham chain of the first kind of length $6$:
::$\tuple {89, 179, 359, 719, 1439, 2879}$
:The $14$th safe prime after $5$, $7$, $11$, $23$, $47$, $59$, $83$, $107$, $167$, $179$, $227$, $263$, $347$:
::$359 = 2 \times 179 + 1$
:The $19$th emirp after $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$, $107$, $113$, $149$, $157$, $167$, $179$, $199$, $311$, $337$, $347$
:The $21$st Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$, $173$, $179$, $191$, $233$, $239$, $251$, $281$, $293$:
::$2 \times 359 + 1 = 719$, which is prime.
== Also see ==
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:359
36,363,636,364

== Number ==
$36 \, 363 \, 636 \, 364$ is:
:$2^2 \times 11 \times 23 \times 4093 \times 8779$
:Its square can be split into two identical halves:
::$36 \, 363 \, 636 \, 364 = 1 \, 322 \, 314 \, 049 \, 613 \, 223 \, 140 \, 496$
== Also see ==
* Number whose Square is in 2 Identical Halves
== Sources ==
* : $36,363,636,364$
* : $36,363,636,364$
Category:Specific Numbers
Category:36,363,636,364
36,365

== Number ==
$36 \, 365$ (thirty-six thousand, three hundred and sixty-five) is:
:$5 \times 7 \times 1039$
:The $6$th integer after $428$, $573$, $727$, $846$, $7810$ whose square has a decimal representation consisting of the concatenation of $2$ consecutive increasing integers:
::$36 \, 365^2 = 1 \, 322 \, 413 \, 225$
:The $9$th integer after $91$, $428$, $573$, $727$, $846$, $7810$, $9079$, $9901$ whose square has a decimal representation consisting of the concatenation of $2$ consecutive integers:
::$36 \, 365^2 = 1 \, 322 \, 413 \, 225$
== Also see ==
* 
* 
Category:Specific Numbers
Category:36,365
360

__NOTOC__
== Number ==
$360$ (three hundred and sixty) is:
:$2^3 \times 3^2 \times 5$
:The $1$st number whose ratio to aliquot sum is $4 : 9$:
::$\dfrac {\map {\sigma_1} {360} - 360} {360} = \dfrac 9 4$
:where $\sigma_1$ denotes the divisor sum function.
:The $13$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$:
::$\map {\sigma_0} {360} = 24$
:The $13$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$:
::$\dfrac {\map {\sigma_1} {360} } {360} = \dfrac {1170} {360} = 3 \cdotp 25$
:The $16$th positive integer after $64$, $96$, $128$, $144$, $160$, $192$, $216$, $224$, $240$, $256$, $288$, $320$, $324$, $336$, $352$ with $6$ or more prime factors:
::$360 = 2 \times 2 \times 2 \times 3 \times 3 \times 5$
:The $33$rd highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $120$, $144$, $168$, $180$, $210$, $216$, $240$, $288$, $300$, $336$:
::$\map {\sigma_1} {360} = 1170$
:The divisor sum of $120$:
::$\map {\sigma_1} {120} = 360 = 3 \times 120$
== Also see ==
* Ratio of 360 to Aliquot Sum
* 
* 
* 
* 
* 
== Historical Note ==
Category:Specific Numbers
Category:360
360/Historical Note

== Historical Note on $360$ (Three Hundred and Sixty) ==
There are $360$ degrees in a full angle.
This appears to have been first done by .
$360$ is very approximately equal to the number of days in a year, which goes some way towards explaining this division of the circle.
Each of the signs of the Zodiac were divided into $30$ degrees, each one corresponding to approximately one day's travel of the sun around the ecliptic.
== Sources ==
* : $360$
* : $360$
Category:Historical Notes
3600

== Number ==
$3600$ (three thousand, six hundred) is:
:$2^4 \times 3^2 \times 5^2$
:The $22$nd square number after $1$, $4$, $36$, $121$, $144$, $256$, $\ldots$, $1936$, $2304$, $2704$, $2916$, $3136$ to be the divisor sum value of some (strictly) positive integer:
::$3600 = \map {\sigma_1} {1080}$
:The $49$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $2209$, $2304$, $2500$, $2809$, $2986$, $3136$, $3364$, $3481$, $3600$, $\ldots$
:The $60$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $2304$, $2401$, $2500$, $2601$, $2704$, $2809$, $2916$, $3025$, $3136$, $3249$, $3364$, $3481$:
::$3600 = 60 \times 60$
== Also see ==
* 
* 
* 
== Historical Note ==
== Sources ==
* : $3600$
* : $3600$
Category:Specific Numbers
Category:3600
3600/Historical Note

== Historical Note on $3600$ (Three Thousand, Six Hundred) ==
There are $3600$ seconds of time in an hour.
There are $3600$ seconds of angle in an degree.
There are $3600$ minutes of angle in a $60$ degree angle.
These divisions date back to the time of the , who used a $60$-based number system for their mathematics and astronomy.
== Also see ==
* Definition:Sexagesimal System
== Sources ==
* : $3600$
* : $3600$
Category:Historical Notes
3605

== Number ==
$3605$ (three thousand, six hundred and five) is:
:$5 \times 7 \times 103$
:The $35$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $2296$, $2465$, $2640$, $2821$, $3008$, $3201$, $3400$:
::$3605 = \ds \sum_{k \mathop = 1}^{35} \paren {6 k - 5} = 35 \paren {3 \times 35 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:3605
360 divides a^2 (a^2 - 1) (a^2 - 4)

== Theorem ==
Let $a \in \Z$ be an integer.
Then:
:$360 \divides a^2 \paren {a^2 - 1} \paren {a^2 - 4}$
where $\divides$ denotes divisibility.
== Proof ==
By Difference of Two Squares:
:$a^2 \paren {a^2 - 1} \paren {a^2 - 4} = a \paren {a - 2} \paren {a - 1} a \paren {a + 1} \paren {a + 2}$
We have that $a - 2, a - 1, a, a + 1, a + 2$ are $5$ consecutive integers.
Hence from Product of 5 Consecutive Integers is Divisible by 120:
:$120 \divides a \paren {a^2 - 1} \paren {a^2 - 4}$
and so:
:$120 \divides a^2 \paren {a^2 - 1} \paren {a^2 - 4}$
As $120 = 2^3 \cdot 3 \cdot 5$, it suffices to show that
:$9 \divides a^2 \paren {a^2 - 1} \paren {a^2 - 4}$
Consider the following 3 cases.
If $a \in 3 \Z$, then $9 \divides a^2$.
If $a \in 3 \Z + 1$, then $a-1, a+2 \in 3 \Z$, so that $9 \divides \paren {a-1} \paren {a+2}$.
If $a \in 3 \Z + 2$, then $a-2, a+1 \in 3 \Z$, so that $9 \divides \paren {a-2} \paren {a+1}$.
== Sources ==
* : Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor: Problems $2.2$: $15 \ \text {(d)}$
Category:Examples of Divisors of Integers
361

== Number ==
$361$ (three hundred and sixty-one) is:
:$19^2$
:The $3$rd square after $49$, $169$ whose decimal representation can be split into two parts which are each themselves square:
::$361 = 19^2$; $36 = 6^2$, $1 = 1^2$
:The $8$th square lucky number:
::$1, 9, 25, 49, 169, 289, 361, \ldots$
:The $19$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $100$, $121$, $144$, $169$, $196$, $225$, $256$, $289$, $324$:
::$361 = 19 \times 19$
:The $32$nd powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $144$, $169$, $196$, $200$, $216$, $225$, $243$, $256$, $288$, $289$, $324$, $343$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:361
3610

== Number ==
$3610$ (three thousand, six hundred and ten) is:
:$2 \times 5 \times 19^2$
:The $19$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$, $196$, $288$, $405$, $550$, $726$, $936$, $1183$, $1470$, $1800$, $2176$, $2601$, $3078$:
::$3610 = \ds \sum_{k \mathop = 1}^{19} \dfrac {k \paren {3 k - 1} } 2 = \dfrac {19^2 \paren {19 + 1} } 2$
:The $20$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$, $469$, $546$, $974$, $1963$, $3507$, $3610$
== Also see ==
* 
* 
== Historical Note ==
== Sources ==
* : $3610! - 1$
Category:Specific Numbers
Category:3610
362

== Number ==
$362$ (three hundred and sixty-two) is:
:$2 \times 181$
:The $3$rd positive integer after $1$, $87$ whose divisor sum of its Euler $\phi$ value equals its divisor sum:
::$\map {\sigma_1} {\map \phi {362} } = \map {\sigma_1} {180} = 546 = \map {\sigma_1} {362}$
:The index (after $2$, $3$, $6$, $30$, $75$, $81$, $115$, $123$, $249$) of the $10$th Woodall prime:
::$362 \times 2^{362} - 1$
:The $36$th noncototient after $10$, $26$, $34$, $50$, $\ldots$, $290$, $292$, $298$, $310$, $326$, $340$, $344$, $346$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 362$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:362
362,880

== Number ==
$362 \, 880$ (three hundred and sixty-two thousand, eight hundred and eighty) is:
:$2^7 \times 3^4 \times 5 \times 7$
:The $9$th factorial after $1$, $2$, $6$, $24$, $120$, $720$, $5040$, $40 \, 320$:
::$362 \, 880 = 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$
:Can be expressed as:
::$9! = 7! \times 3! \times 3! \times 2!$
== Also see ==
* 
== Sources ==
* : $362,880$
* : $362,880$
Category:Specific Numbers
Category:362,880
363

== Number ==
$363$ (three hundred and sixty-three) is:
:$3 \times 11^2$
:The $7$th palindromic integer after $0$, $1$, $2$, $3$, $11$, $77$ which is the index of a palindromic triangular number
::$T_{363} = 66 \, 066$
== Also see ==
* 
== Sources ==
* : $363,474,363$
Category:Specific Numbers
Category:363
363,474,363

== Number ==
$363 \, 474 \, 363$ is:
:$3 \times 7 \times 17 \, 308 \, 303$
:The $13$th palindromic integer after $0$, $1$, $2$, $3$, $11$, $77$, $363$, $1111$, $2662$, $111 \, 111$, $246 \, 642$, $11 \, 111 \, 111$ which is the index of a palindromic triangular number
::$T_{363 \, 474 \, 363} = 66 \, 056 \, 806 \, 460 \, 865 \, 066$
== Also see ==
* 
== Sources ==
* : $363,474,363$
Category:Specific Numbers
Category:363,474,363
364

== Number ==
$364$ (three hundred and sixty-four) is:
:$2^2 \times 7 \times 13$
:The $12$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$, $165$, $220$, $286$:
::$364 = \ds \sum_{k \mathop = 1}^{12} \frac {k \paren {k + 1} } 2 = \dfrac {12 \paren {12 + 1} \paren {12 + 2} } 6$
:Hence the total number of gifts in .
:The $21$st number whose divisor sum is square:
:
== Also see ==
* 
* 
Category:Specific Numbers
Category:364
365

__NOTOC__
== Number ==
$365$ (three hundred and sixty-five) is:
:$5 \times 73$
:The $1$st positive integer which is the sum of both $2$ and $3$ consecutive non-zero square numbers:
::$365 = 10^2 + 11^2 + 12^2 = 13^3 + 14^2$
:The $18$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$, $85$, $89$, $101$, $125$, $145$, $149$, $245$, $265$ such that the Fibonacci number $F_n$ ends in $n$
== Also see ==
* 
* 
== Historical Note ==
== Sources ==
* : $365$
Category:Specific Numbers
Category:365
3654

== Number ==
$3654$ (three thousand, six hundred and fifty-four) is:
:$2 \times 3^2 \times 7 \times 29$
:The $27$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $\ldots$, $816$, $969$, $1140$, $1330$, $1540$, $1771$, $2024$, $2300$, $2600$, $2925$, $3276$:
::$3654 = \ds \sum_{k \mathop = 1}^{27} \frac {k \paren {k + 1} } 2 = \dfrac {27 \paren {27 + 1} \paren {27 + 2} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:3654
3655

== Number ==
$3655$ (three thousand, six hundred and fifty-five) is:
:$5 \times 17 \times 43$
:The $1$st of the $2$nd quadruple of consecutive integers which all have an equal divisors:
::$\map {\sigma_0} {3655} = \map {\sigma_0} {3656} = \map {\sigma_0} {3657} = \map {\sigma_0} {3658} = 8$
:The $43$rd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $2145$, $2278$, $2415$, $2556$, $2701$, $2850$, $3003$, $3160$, $3321$, $3486$:
::$3655 = \ds \sum_{k \mathop = 1}^{43} \paren {4 k - 3} = 43 \paren {2 \times 43 - 1}$
:The $85$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $2701$, $2775$, $2850$, $2926$, $3003$, $3081$, $3160$, $3240$, $3321$, $3403$, $3486$, $3570$:
::$3655 = \ds \sum_{k \mathop = 1}^{85} k = \dfrac {85 \times \paren {85 + 1} } 2$
== Also see ==
* 
* 
* 
== Sources ==
* : $242$
Category:Specific Numbers
Category:3655
366

== Number ==
$366$ (three hundred and sixty-six) is:
:$2 \times 3 \times 61$
:The $4$th integer solution to $\map {\sigma_1} n = \map {\sigma_1} {n + 2}$ after $33$, $54$, $284$:
::$\map {\sigma_1} {366} = 744 = \map {\sigma_1} {368}$
:The $37$th noncototient after $10$, $26$, $34$, $50$, $\ldots$, $290$, $292$, $298$, $310$, $326$, $340$, $344$, $346$, $362$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 366$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $39$th sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$, $357$:
::$366 = 2 \times 3 \times 61$
== Also see ==
* 
* 
* 
== Historical Note ==
Category:Specific Numbers
Category:366
366,556

== Number ==
$366 \, 556$ (three hundred and sixty-six thousand, five hundred and fifty-six) is:
:$2^2 \times 91 \, 639$
:The $13$th term of a sociable chain of order $28$ whose smallest term is $14 \, 316$:
::$14 \, 316$, $19 \, 116$, $31 \, 704$, $47 \, 616$, $83 \, 328$, $177 \, 792$, $295 \, 488$, $629 \, 072$, $589 \, 786$, $294 \, 896$, $358 \, 336$, $418 \, 904$, $366 \, 556$, $274 \, 924$, $275 \, 444$, $243 \, 760$, $376 \, 736$, $381 \, 028$, $285 \, 778$, $152\, 990$, $122 \, 410$, $97 \, 946$, $48 \, 976$, $45 \, 946$, $22 \, 976$, $22 \, 744$, $19 \, 916$, $17 \, 716$, $14 \, 316$, $\ldots$
== Also see ==
* 
Category:Specific Numbers
Category:366,556
367

== Number ==
$367$ (three hundred and sixty-seven) is:
:The $73$rd prime number
:The larger of the $2$nd pair of primes whose prime gap is $8$:
::$367 - 359 = 8$
:The $3$rd positive integer $n$ after $157, 262$ for which $\map \phi {2 n + 1} < \map \phi {2 n}$:
::$\map \phi {2 \times 367 + 1} = 336$, $\map \phi {2 \times 367} = 366$
:The $14$th of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 13^2 + 29 = 367$ ()
:The $26$th long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $181$, $193$, $223$, $229$, $233$, $257$, $263$, $269$, $313$, $337$
:The $28$th left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $197$, $223$, $283$, $313$, $317$, $337$, $347$, $353$
== Also see ==
* 
* 
* 
* 
* 
== Sources ==
* : $157$
Category:Specific Numbers
Category:367
3676

== Number ==
$3676$ (three thousand, six hundred and seventy-six) is:
:$2^2 \times 919$
:The $19$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
::$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $370$, $526$, $706$, $730$, $771$, $1255$, $1351$, $1414$, $1906$, $2986$, $3676$, $\ldots$
== Also see ==
* 
Category:Specific Numbers
Category:3676
368

== Number ==
$368$ (three hundred and sixty-eight) is:
:$2^4 \times 23$
:The $7$th primitive abundant number after $20$, $70$, $88$, $104$, $272$, $304$:
::$1 + 2 + 4 + 8 + 16 + 23 + 46 + 92 + 184 = 376 > 368$
:The $9$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $272$, $304$, $350$:
::$368 = 1 + 2 + 4 + 16 + 23 + 46 + 92 + 184$
== Also see ==
* 
* 
Category:Specific Numbers
Category:368
369

== Number ==
$369$ (three hundred and sixty-nine) is:
:$3^2 \times 41$
:The number of distinct free octominoes
:The magic constant of a magic square of order $9$, after $1$, $(5)$, $15$, $34$, $65$, $111$, $175$, $260$:
::$369 = \ds \dfrac 1 9 \sum_{k \mathop = 1}^{9^2} k = \dfrac {9 \paren {9^2 + 1} } 2$
== Also see ==
* 369 Octominoes
* 
* 
== Sources ==
* : $35$
* : $35$
Category:Specific Numbers
Category:369
369,119

== Number ==
$369 \, 119$ (three hundred and sixty-nine thousand, one hundred and nineteen) is:
:The $31 \, 464$th prime number
:The $4$th prime number after $2$, $5$, $71$ which divides the sum of all smaller primes:
::$15 \, 001 \times 369 \, 119 = 5 \, 537 \, 154 \, 119 = 2 + 3 + 5 + \cdots + 369 \, 079 + 369 \, 097$
== Also see ==
* 
* 
== Sources ==
* : $369,119$
* : $369,119$
Category:Specific Numbers
Category:369,119