nyuuzyou/wikis huggingface dataset:
136

== Number ==
$136$ (one hundred and thirty-six) is:
:$2^3 \times 17$
:The $2$nd of the $4$ cubic recurring digital invariants after $55$:
::$136 \to 244 \to 136$
:The total of all the entries in a magic square of order $4$, after $1$, $(10)$, $45$:
::$136 = \ds \sum_{k \mathop = 1}^{4^2} k = \dfrac {4^2 \paren {4^2 + 1} } 2$
:The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $12$ different ways
:The $16$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$, $78$, $91$, $105$, $120$:
::$136 = \ds \sum_{k \mathop = 1}^{16} k = \dfrac {16 \times \paren {16 + 1} } 2$
:The $56$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$, $112$, $116$, $124$ which cannot be expressed as the sum of distinct pentagonal numbers.
== Also see ==
* 
* 
* 
* 
* 
== Sources ==
* : $136$
* : $136$
Category:Specific Numbers
Category:136
1364

== Number ==
$1364$ (one thousand, three hundred and sixty-four) is:
:$2^2 \times 11 \times 31$
:The $15$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$, $29$, $47$, $76$, $123$, $199$, $322$, $521$, $843$:
::$1364 = 521 + 843$
== Also see ==
* 
Category:Specific Numbers
Category:1364
1365

== Number ==
$1365$ (one thousand, three hundred and sixty-five) is:
:$3 \times 5 \times 7 \times 13$
:The $12$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$, $330$, $495$, $715$, $1001$:
::$1365 = \ds \sum_{k \mathop = 1}^{12} \dfrac {k \paren {k + 1} \paren {k + 2} } 6 = \dfrac {12 \paren {12 + 1} \paren {12 + 2} \paren {12 + 3} } {24}$
:The $30$th second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $610$, $672$, $737$, $805$, $876$, $950$, $1027$, $1107$, $1190$, $1276$:
::$1365 = \dfrac {30 \paren{3 \times 30 + 1} } 2$
:The $60$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $925$, $950$, $1001$, $1027$, $1080$, $1107$, $1162$, $1190$, $1247$, $1276$, $1335$:
::$1365 = \dfrac {30 \paren {3 \times 30 + 1} } 2$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1365
1367

== Number ==
$1367$ (one thousand, three hundred and sixty-seven) is:
:The $219$th prime number
:The $20$th balanced prime after $5$, $53$, $157$, $173$, $211$, $257$, $263$, $373$, $563$, $593$, $607$, $653$, $733$, $947$, $977$, $1103$, $1123$, $1187$, $1223$:
::$1367 = \dfrac {1361 + 1373} 2$
:The $31$st safe prime after $5$, $7$, $11$, $23$, $47$, $\ldots$, $839$, $863$, $887$, $983$, $1019$, $1187$, $1283$, $1307$, $1319$:
::$1367 = 2 \times 683 + 1$
:The $57$th left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $743$, $773$, $797$, $823$, $853$, $883$, $937$, $947$, $953$, $967$, $983$, $997$, $1223$, $1283$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:1367
1369

== Number ==
$1369$ (one thousand three hundred and sixty-nine) is:
:$37^2$
:The $37$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $625$, $676$, $729$, $784$, $841$, $900$, $961$, $1024$, $1089$, $1156$, $1225$, $1296$:
::$1369 = 37 \times 37$
== Also see ==
* 
Category:Specific Numbers
Category:1369
137

== Number ==
$137$ (one hundred and thirty-seven) is:
:The $33$rd prime number
:The $4$th Stern number after $1$, $3$, $17$
:The $4$th Stern prime after $1$, $3$, $17$
:The smaller of the $11$th pair of twin primes, with $139$
:The $17$th left-truncatable prime after $2$, $3$, $5$, $7$, $13$, $17$, $23$, $37$, $43$, $47$, $53$, $67$, $73$, $83$, $97$, $113$
:The $57$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$, $112$, $116$, $124$, $136$ which cannot be expressed as the sum of distinct pentagonal numbers.
== Also see ==
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:137
137,438,953,471

== Number ==
$137 \, 438 \, 953 \, 471$ is:
:$223 \times 616 \, 318 \, 177$
:The $4$th Mersenne number after $2047$, $8 \, 388 \, 607$, $536 \, 870 \, 911$ which is composite:
::$137 \, 438 \, 953 \, 471 = 2^{37} - 1 = 223 \times 616 \, 318 \, 177$
:The $12$th Mersenne number after $3$, $7$, $31$, $127$, $2047$, $8191$, $131 \, 071$, $524 \, 287$, $8 \, 388 \, 607$, $536 \, 870 \, 911$, $2 \, 147 \, 483 \, 647$:
::$137 \, 438 \, 953 \, 471 = 2^{37} - 1$
== Historical Note ==
== Also see ==
* 
* 
Category:Specific Numbers
Category:137,438,953,471
137,438,953,471/Historical Note

== Historical Note on $137 \, 438 \, 953 \, 471$ ==
$137 \, 438 \, 953 \, 471$ was the $3$rd Mersenne number to be demonstrated composite.
This was done in $1640$ by , who demonstrated it had $223$ as a divisor.
It is in fact the $4$th Mersenne number in sequence to be composite.
However, the status of the $3$rd such composite Mersenne number, $536 \, 870 \, 911$, was not established until 's work in $1732$.
== Sources ==
* : Preface
Category:Historical Notes
1373

== Number ==
$1373$ (one thousand, three hundred and seventy-three) is:
:The $220$th prime number
:The smaller of the $19$th pair of primes whose prime gap is $8$:
::$1381 - 1373 = 8$
:The $58$th left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $743$, $773$, $797$, $823$, $853$, $883$, $937$, $947$, $953$, $967$, $983$, $997$, $1223$, $1283$, $1367$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1373
1375

== Number ==
$1375$ (one thousand, three hundred and seventy-five) is:
:$5^3 \times 11$
:The $1$st term of the $1$st triplet of consecutive positive integers each of which is divisible by a cube greater than $1$:
::$1375 = 11 \times 5^3$, $1376 = 172 \times 2^3$, $1377 = 51 \times 3^3$
== Also see ==
* 
== Sources ==
* : $1375$
* : $1375$
Category:Specific Numbers
Category:1375
1376

== Number ==
$1376$ (one thousand, three hundred and seventy-six) is:
:$2^5 \times 43$
:The $2$nd term of the $1$st triplet of consecutive positive integers each of which is divisible by a cube greater than $1$:
::$1375 = 11 \times 5^3$, $1376 = 172 \times 2^3$, $1377 = 51 \times 3^3$
:The $17$th primitive abundant number after $20$, $70$, $88$, $104$, $272$, $304$, $368$, $464$, $550$, $572$, $650$, $748$, $836$, $945$, $1184$, $1312$:
::$1 + 2 + 4 + 8 + 16 + 32 + 43 + 86 + 172 + 344 + 688 = 1396 > 1376$
:The $24$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $\ldots$, $572$, $650$, $748$, $770$, $910$, $945$, $1184$, $1190$, $1312$, $1330$:
::$1376 = 1 + 2 + 8 + 32 + 43 + 86 + 172 + 344 + 688$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1376
1377

== Number ==
$1377$ (one thousand, three hundred and seventy-seven) is:
:$3^4 \times 17$
:The $3$rd term of the $1$st triplet of consecutive positive integers each of which is divisible by a cube greater than $1$:
::$1375 = 11 \times 5^3$, $1376 = 172 \times 2^3$, $1377 = 51 \times 3^3$
== Also see ==
* 
Category:Specific Numbers
Category:1377
1378

== Number ==
$1378$ (one thousand, three hundred and seventy-eight) is:
:$2 \times 13 \times 53$
:The $52$nd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $990$, $1035$, $1081$, $1128$, $1176$, $1225$, $1275$, $1326$:
::$1378 = \ds \sum_{k \mathop = 1}^{52} k = \dfrac {52 \times \paren {52 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:1378
1379

== Number ==
$1379$ (one thousand, three hundred and seventy-nine) is:
:$7 \times 197$
:The magic constant of a magic square of order $14$, after $1$, $(5)$, $15$, $34$, $65$, $111$, $175$, $260$, $369$, $505$, $671$, $870$, $1105$:
::$\ds 1379 = \dfrac 1 {14} \sum_{k \mathop = 1}^{14^2} k = \dfrac {14 \paren {14^2 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:1379
138

== Number ==
$138$ (one hundred and thirty-eight) is:
:$2 \times 3 \times 23$
:The $11$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$:
::$138 = 2 \times 3 \times 23$
:Its aliquot sequence terminates in $1$ after $177$ steps.
== Also see ==
* Aliquot Sequence starting from $138$
* 
== Sources ==
* : $276$
* 
* : $276$
Category:Specific Numbers
Category:138
1381

== Number ==
$1381$ (one thousand three hundred and eighty-one) is:
:The $221$st prime number
:The larger of the $19$th pair of primes whose prime gap is $8$:
::$1381 - 1373 = 8$
:The $27$th of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 26^2 + 29 = 1381$ ()
== Also see ==
* 
* 
Category:Specific Numbers
Category:1381
1387

== Number ==
$1387$ (one thousand, three hundred and eighty-seven) is:
:$19 \times 73$
:The $22$nd centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $\ldots$, $817$, $919$, $1027$, $1141$, $1261$:
::$1387 = \ds 1 + \sum_{k \mathop = 1}^{22 - 1} 6 k = 22^3 - 21^3$
:The $5$th Poulet number after $341$, $561$, $645$, $1105$:
::$2^{1387} \equiv 2 \pmod {1387}$: $1387 = 19 \times 73$
== Also see ==
* 
* 
Category:Specific Numbers
Category:1387
139

== Number ==
$139$ (one hundred and thirty-nine) is:
:The $34$th prime number
:The $9$th of $11$ primes of the form $2 x^2 + 11$:
::$2 \times 8^2 + 11 = 139$ ()
:The larger of the $11$th pair of twin primes, with $137$
:The $26$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$:
::$139 \to 1^2 + 3^2 + 9^2 = 1 + 9 + 81 = 91 \to 9^2 + 1^2 = 81 + 1 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$
:The smaller of the $1$st pair of primes whose prime gap is $10$:
::$149 - 139 = 10$
== Also see ==
* 
* 
* 
* 
== Sources ==
* : $139$
* : $139$
Category:Specific Numbers
Category:139
139,854,276

== Number ==
$139 \, 854 \, 276$ (one hundred and thirty-nine million, eight hundred and fifty-four thousand, two hundred and seventy-six) is:
:$2^2 \times 3^8 \times 73^2$
:The $1$st square number which contains all the digits from $1$ to $9$:
::$139 \, 854 \, 276 = 11 \, 826^2$
:The $11 \, 826$th square number:
::$139 \, 854 \, 276 = 11 \, 826 \times 11 \, 826$
== Also see ==
* Smallest Penholodigital Square
* 11,826
* 
== Sources ==
* : $139,854,276$
* : $139,854,276$
Category:Specific Numbers
Category:139,854,276
14

__NOTOC__
== Number ==
$14$ (fourteen) is:
:$2 \times 7$
:The $1$st power of $14$ after the zeroth $1$:
::$14 = 14^1$
:The $1$st positive integer solution to $\map {\sigma_1} n = \map {\sigma_1} {n + 1}$:
::$\map {\sigma_1} {14} = 24 = \map {\sigma_1} {15}$
:where $\sigma_1$ denotes the divisor sum function
:The $1$st nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 14$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $1$st Keith number:
::$1$, $4$, $5$, $9$, $14$, $\ldots$
:The $2$nd integer after $1$ whose divisor sum divided by its Euler $\phi$ value is a square:
::$\dfrac {\map {\sigma_1} {14} } {\map \phi {14} } = \dfrac {24} 6 = 4 = 2^2$
:The $3$rd square pyramidal number after $1$, $5$:
::$14 = 1 + 4 + 9 = \dfrac {3 \paren {3 + 1} \paren {2 \times 3 + 1} } 6$
:The $3$rd positive integer after $1$, $3$ of which the product of its Euler $\phi$ function and its divisor count equals its divisor sum:
::$\map \phi {14} \map {\sigma_0} {14} = 6 \times 4 = 24 = \map {\sigma_1} {14}$
:The $1$st of the $4$th pair of consecutive integers whose product is a primorial:
::$14 \times 15 = 210 = 7 \#$
:The $4$th Catalan number after $(1)$, $1$, $2$, $5$:
::$14 = \dfrac 1 {4 + 1} \dbinom {2 \times 4} 4 = \dfrac 1 5 \times 70$
:The number of different representations of $1$ as the sum of $4$ unit fractions.
:The $5$th semiprime after $4$, $6$, $9$, $10$:
::$14 = 2 \times 7$
:The $6$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$
:The $6$th and last after $1$, $2$, $5$, $6$, $10$ of $6$ integers $n$ such that the alternating group $A_n$ is ambivalent
:The $7$th even number after $2$, $4$, $6$, $8$, $10$, $12$ which cannot be expressed as the sum of $2$ composite odd numbers.
:The $9$th positive integer after $2$, $3$, $4$, $7$, $8$, $9$, $10$, $11$ which cannot be expressed as the sum of distinct pentagonal numbers.
:The $11$th after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $10$, $12$ of $21$ integers which can be represented as the sum of two primes in the maximum number of ways
:The $12$th (strictly) positive integer after $1$, $2$, $3$, $4$, $6$, $7$, $8$, $9$, $10$, $12$, $13$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
:The $12$th integer $n$ after $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $13$ such that $2^n$ contains no zero in its decimal representation:
::$2^{14} = 16 \, 384$
:There exist $14$ distinct Bravais lattices.
=== Kuratowski's Closure-Complement Problem ===
== Also see ==
* Kuratowski's Closure-Complement Problem
* 14 Distinct Bravais Lattices
* 12 times Divisor Sum of 12 equals 14 times Divisor Sum of 14
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
== Historical Note ==
== Sources ==
* : Glossary
* : $14$
* : Glossary
* : $14$
* 
* 
Category:Specific Numbers
Category:14
14,182,439,040

== Number ==
$14 \, 182 \, 439 \, 040$ is:
:$2^7 \times 3^4 \times 5 \times 7 \times 11^2 \times 17 \times 19$
:The $1$st multiply perfect of order $5$:
::$\map {\sigma_1} {14 \, 182 \, 439 \, 040} = 70 \, 912 \, 195 \, 200 = 5 \times 14 \, 182 \, 439 \, 040$
== Also see ==
* Smallest Multiply Perfect Number of Order 5
== Sources ==
* : $14,182,439,040$
Category:Specific Numbers
Category:14,182,439,040
14,264

== Number ==
$14 \, 264$ (fourteen thousand, two hundred and sixty-four) is:
:$2^3 \times 1783$
:The $5$th term of a sociable chain of order $5$ whose smallest term is $12 \, 496$:
::$12 \, 496 \to 14 \, 288 \to 15 \, 472 \to 14 \, 536 \to 14 \, 264 \to 12 \, 496$
== Also see ==
* 
Category:Specific Numbers
Category:14,264
14,288

== Number ==
$14 \, 288$ (twelve thousand, four hundred and ninety-six) is:
:$2^4 \times 19 \times 47$
:The $2$nd term of a sociable chain of order $5$ whose smallest term is $12 \, 496$:
::$12 \, 496 \to 14 \, 288 \to 15 \, 472 \to 14 \, 536 \to 14 \, 264 \to 12 \, 496$
== Also see ==
* 
Category:Specific Numbers
Category:14,288
14,316

== Number ==
$14 \, 316$ (fourteen thousand, three hundred and sixteen) is:
:$2^2 \times 3 \times 1193$
:The $1$st 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 ==
* 
== Sources ==
* : $14,316$
* : $14,316$
Category:Specific Numbers
Category:14,316
14,348,907

== Number ==
$14 \, 348 \, 907$ (fourteen million, three hundred and forty-eght thousand, nine hundred and seven) is:
:$3^{15}$
:The $243$rd cube number:
::$14 \, 348 \, 907 = 243 \times 243 \times 243$
:The $27$th $5$th power:
::$14 \, 348 \, 907 = 27 \times 27 \times 27 \times 27 \times 27$
:The $15$th power of $3$ after $(1)$, $3$, $9$, $27$, $81$, $243$, $729$, $2187$, $6561$, $19 \, 683$, $59 \, 049$, $177 \, 147$, $531 \, 441$, $1 \, 594 \, 323$, $4 \, 782 \, 969$:
::$14 \, 348 \, 907 = 3^{15}$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:14,348,907
14,536

== Number ==
$14 \, 536$ (fourteen thousand, five hundred and thirty-six) is:
:$2^3 \times 23 \times 79$
:The $4$th term of a sociable chain of order $5$ whose smallest term is $12 \, 496$:
::$12 \, 496 \to 14 \, 288 \to 15 \, 472 \to 14 \, 536 \to 14 \, 264 \to 12 \, 496$
== Also see ==
* 
Category:Specific Numbers
Category:14,536
14,595

== Number ==
$14 \, 595$ (fourteen thousand, five hundred and ninety-five) is:
:$3 \times 5 \times 7 \times 139$
:The larger of the $7$th amicable pair and the $1$st odd amicable pair, with $12 \, 285$:
::$\map {\sigma_1} {12 \, 285} = \map {\sigma_1} {14 \, 595} = 26 \, 880 = 12 \, 285 + 14 \, 595$
== Also see ==
* 
* 
== Sources ==
* : $12,285$
* : $12,285$
Category:Specific Numbers
Category:14,595
14,641

== Number ==
$14 \, 641$ (fourteen thousand, six hundred and forty-one) is:
:$11^4$
:The $4$th power of $11$ after $(1)$, $11$, $121$, $1331$:
::$14 \, 641 = 11^4$
:The $11$th fourth power after $1$, $16$, $81$, $256$, $625$, $1296$, $2401$, $4096$, $6561$, $10 \, 000$:
::$14 \, 641 = 11 \times 11 \times 11 \times 11$
:The $121$st square number:
::$14 \, 641 = 121 \times 121$
== Also see ==
* Fourth Power of 11 is Palindromic
* 
* 
* 
== Sources ==
* : $121$
* : $121$
Category:Specific Numbers
Category:14,641
14,833

== Number ==
$14 \, 833$ (fourteen thousand, eight hundred and thirty-three) is:
:$7 \times 13 \times 163$
:The $8$th subfactorial after $0$, $1$, $2$, $9$, $44$, $265$, $1854$:
::$14 \, 833 = \mathop !8 = 8! \paren {1 - \dfrac 1 {1!} + \dfrac 1 {2!} - \dfrac 1 {3!} + \dfrac 1 {4!} - \dfrac 1 {5!} + \dfrac 1 {6!} - \dfrac 1 {7!} + \dfrac 1 {8!} }$
== Also see ==
* 
Category:Specific Numbers
Category:14,833
140

== Number ==
$140$ (one hundred and forty) is:
:$2^2 \times 5 \times 7$
:With $195$, an element of the $2$nd quasiamicable pair:
::$\map {\sigma_1} {140} = \map {\sigma_1} {195} = 336 = 140 + 195 + 1$
:The $4$th Ore number after $1, 6, 28$:
::$\dfrac {140 \times \map {\sigma_0} {140} } {\map {\sigma_1} {140} } = 5$
:and the $3$rd after $1, 6$ whose divisors also have an arithmetic mean which is an integer:
::$\dfrac {\map {\sigma_1} {140} } {\map {\sigma_0} {140} } = 28$
:The $7$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $91$:
::$140 = 1 + 4 + 9 + 16 + 25 + 36 + 49$
:The $10$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
::$\map {\sigma_0} {140} = 12$, $\map \phi {140} = 48$, $\map {\sigma_1} {140} = 336$
== Also see ==
* 
* 
* 
* 
* 
== Sources ==
* : $140$
Category:Specific Numbers
Category:140
1404

== Number ==
$1404$ (one thousand, four hundred and four) is:
:$2^2 \times 3^3 \times 13$
:The $24$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $\ldots$, $874$, $970$, $1071$, $1177$, $1288$:
::$1404 = \ds \sum_{k \mathop = 1}^{24} \paren {5 k - 4} = \dfrac {24 \paren {5 \times 24 - 3} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:1404
1408

== Number ==
$1408$ (one thousand, four hundred and eight) is:
:$2^7 \times 11$
:The $22$nd octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $645$, $736$, $833$, $936$, $1045$, $1160$, $1281$:
::$1408 = \ds \sum_{k \mathop = 1}^{22} \paren {6 k - 5} = 22 \paren {3 \times 22 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:1408
1409

== Number ==
$1409$ (one thousand, four hundred and nine) is:
:The $223$rd prime number
:The larger of the $24$th pair of primes whose prime gap is $10$:
::$1409 - 1399 = 10$
:The $46$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $761$, $809$, $911$, $953$, $1013$, $1019$, $1031$, $1049$, $1103$, $1223$, $1229$, $1289$:
::$2 \times 1409 + 1 = 2819$, which is prime.
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1409
141

== Number ==
$141$ (one hundred and forty-one) is:
:$3 \times 47$
:The index of the $2$nd Cullen prime after $1$:
::$141 \times 2^{141} + 1$
:The $8$th palindromic lucky number:
::$1$, $3$, $7$, $9$, $33$, $99$, $111$, $141$, $\ldots$
:The $27$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.
:The $30$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $105$, $111$, $115$, $127$, $129$, $133$, $135$, $141$, $\ldots$
:The $58$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$, $112$, $116$, $124$, $136$, $137$ which cannot be expressed as the sum of distinct pentagonal numbers.
== Also see ==
* 
* 
* 
* 
* 
== Sources ==
* : $141$
* : $141$
Category:Specific Numbers
Category:141
1414

== Number ==
$1414$ (one thousand, four hundred and fourteen) is:
:$2 \times 7 \times 101$
:The $16$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
::$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $370$, $526$, $706$, $730$, $771$, $1255$, $1351$, $1414$, $\ldots$
:The $33$rd positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $706$, $730$, $771$, $784$, $841$, $1024$, $1089$, $1225$, $1255$, $1351$, $1414$, $\ldots$
== Also see ==
* 
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Category:Specific Numbers
Category:1414
1416

== Number ==
$1416$ (one thousand four hundred and sixteen) is:
:$2^3 \times 3 \times 59$
:The $49$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $1176$, $1184$, $1197$, $1212$, $1296$, $1311$, $1332$, $1344$:
::$1416 = 59 \times 24 = 59 \times \paren {1 \times 4 \times 1 \times 6}$
== Also see ==
* 
Category:Specific Numbers
Category:1416
142

== Number ==
$142$ (one hundred and forty-two) is:
:$2 \times 71$
:The $5$th positive integer after $1$, $7$, $102$, $110$ the sum of whose divisors is a cube:
::$\map {\sigma_1} {142} = 216 = 6^3$
:The $18$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$, $74$, $76$, $86$, $90$, $94$, $98$, $114$, $118$, $122$, $124$, $134$:
::$\nexists m \in \Z_{>0}: \map \phi m = 142$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $59$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$, $112$, $116$, $124$, $136$, $137$, $141$ which cannot be expressed as the sum of distinct pentagonal numbers.
== Also see ==
* 
* 
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Category:Specific Numbers
Category:142
142,857

== Number ==
$142 \, 857$ (one hundred and forty-two thousand, eight hundred and fifty-seven) is:
:$3^3 \times 11 \times 13 \times 37$
:The $25$th Kaprekar number after $1, 9, 45, 55, 99, 297, \ldots, 38962, 77 \, 778, 82 \, 656, 95 \, 121, 99 \, 999$:
::$142 \, 857^2 = 20 \, 408 \, 122 \, 449 \to 20 \, 408 + 122 \, 449 = 142 \, 857$
:The recurring part of the decimal expansion of the reciprocal of $7$:
::$\dfrac 1 7 = 0 \cdotp \dot 14285 \dot 7$
== Also see ==
* 
== Sources ==
* : $297$
* : $142,857$
* : $297$
* : $142,857$
Category:Specific Numbers
Category:142,857
1426

== Number ==
$1426$ (one thousand, four hundred and twenty-six) is:
:$2 \times 23 \times 31$
:The $31$st pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $925$, $1001$, $1080$, $1162$, $1247$, $1335$:
::$1426 = \ds \sum_{k \mathop = 1}^{31} \paren {3 k - 2} = \dfrac {31 \paren {3 \times 31 - 1} } 2$
:The $61$st generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $925$, $950$, $1001$, $1027$, $1080$, $1107$, $1162$, $1190$, $1247$, $1276$, $1335$, $1365$:
::$1426 = \ds \sum_{k \mathop = 1}^{31} \paren {3 k - 2} = \dfrac {31 \paren {3 \times 31 - 1} } 2$
== Also see ==
* 
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Category:Specific Numbers
Category:1426
143

== Number ==
$143$ (one hundred and forty-three) is:
:$11 \times 13$
:Every positive integer can be expressed as the sum of at most $143$ positive $7$th powers.
:The $58$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $95$, $96$, $102$, $108$, $114$, $119$, $120$, $125$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
== Also see ==
* Hilbert-Waring Theorem for $7$th Powers
* 
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Category:Specific Numbers
Category:143
1430

== Number ==
$1430$ (one thousand, four hundred and thirty) is:
:$2 \times 5 \times 11 \times 13$
:The $8$th Catalan number after $(1)$, $1$, $2$, $5$, $14$, $42$, $132$, $429$:
::$1430 = \dfrac 1 {8 + 1} \dbinom {2 \times 8} 8 = \dfrac 1 9 \times 12 \, 870$
:The $18$th primitive abundant number after $20$, $70$, $88$, $104$, $272$, $304$, $368$, $464$, $550$, $572$, $650$, $748$, $836$, $945$, $1184$, $1312$, $1376$:
::$1 + 2 + 5 + 10 + 11 + 13 + 22 + 26 + 55 + 65 + 110 + 130 + 143 + 286 + 715 = 1594 > 1430$
:The $25$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $\ldots$, $572$, $650$, $748$, $770$, $910$, $945$, $1184$, $1190$, $1312$, $1330$, $1376$:
::$1430 = 1 + 2 + 5 + 13 + 22 + 26 + 55 + 65 + 110 + 130 + 286 + 715$
== Also see ==
* 
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* 
Category:Specific Numbers
Category:1430