nyuuzyou/wikis huggingface dataset:
37

== Number ==
$37$ (thirty-seven) is:
:The $12$th prime number, after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$
:Every positive integer can be expressed as the sum of at most $37$ positive $5$th powers
:The $2$nd integer which has a reciprocal whose period is $3$:
::$\dfrac 1 {37} = 0 \cdotp \dot 02 \dot 7$
:The $3$rd unique period prime after $3$, $11$: its period is $3$:
::$\dfrac 1 {37} = 0 \cdotp \dot 02 \dot 7$
:The $3$rd of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 2^2 + 29 = 37$ ()
:The $4$th centered hexagonal number after $1$, $7$, $19$:
::$37 = 1 + 6 + 12 + 18 = 4^3 - 3^3$
:The $4$th prime number of the form $n^2 + 1$ after $2$, $5$, $17$:
::$37 = 6^2 + 1$
:The $4$th emirp after $13$, $17$, $31$
:The $4$th prime $p$ after $11$, $23$, $29$ such that the Mersenne number $2^p - 1$ is composite
:The $5$th of $5$ primes of the form $2 x^2 + 5$:
::$2 \times 4^2 + 5 = 37$ ()
:The $6$th two-sided prime after $2$, $3$, $5$, $7$, $23$:
::$37$, $3$, $7$ are prime
:The $7$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:
::$0$, $1$, $2$, $3$, $11$, $27$, $37$
:The $8$th right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $29$, $31$
:The $8$th left-truncatable prime after $2$, $3$, $5$, $7$, $13$, $17$, $23$
:The $9$th permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$
:The $11$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $\ldots$
:The $19$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
::$1$, $3$, $5$, $7$, $9$, $11$, $13$, $15$, $17$, $19$, $21$, $23$, $25$, $27$, $29$, $31$, $33$, $35$, $37$, $\ldots$
:The $23$rd positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $26$, $29$, $30$, $31$, $32$, $33$ which cannot be expressed as the sum of distinct pentagonal numbers
:The $27$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $27$, $30$, $31$, $32$, $35$, $36$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
:The $27$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
::$2^{37} = 137 \, 438 \, 953 \, 472$
== Also see ==
* 37 is Second Number whose Period of Reciprocal is 3
* Numbers whose Cyclic Permutations of 3-Digit Multiples are Multiples
* Hilbert-Waring Theorem for $5$th Powers
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== Sources ==
* : $\text I$: The Series of Primes: $1.2$ Prime numbers
* : $37$
* : $37$
Category:Specific Numbers
Category:37
370

== Number ==
$370$ (three hundred and seventy) is:
:$2 \times 5 \times 37$
:The $9$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
::$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $370$, $\ldots$
:The $11$th pluperfect digital invariant after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $153$:
::$3^3 + 7^3 + 0^3 = 27 + 343 + 0 = 370$
:The $17$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $324$, $370$, $\ldots$
:The $40$th sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$, $357$, $366$:
::$370 = 2 \times 5 \times 37$
== Also see ==
* 
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== Sources ==
* : $153$
* : $370$
* : $153$
* : $370$
Category:Specific Numbers
Category:370
371

== Number ==
$371$ (three hundred and seventy-one) is:
:$7 \times 53$
:The $16$th inconsummate number after $62$, $63$, $65$, $75$, $84$, $95$, $161$, $173$, $195$, $216$, $261$, $266$, $272$, $276$, $326$:
::$\nexists n \in \Z_{>0}: n = 371 \times s_{10} \left({n}\right)$
:The $12$th pluperfect digital invariant after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $153$, $370$:
::$3^3 + 7^3 + 1^3 = 27 + 343 + 1 = 371$
== Also see ==
* 
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== Sources ==
* : $153$
* : $371$
* : $153$
* : $371$
Category:Specific Numbers
Category:371
371,293

== Number ==
$371 \, 293$ (three hundred and seventy-one thousand, two hundred and ninety-three) is:
:$13^5$
:The $13$th fifth power after $1$, $32$, $243$, $1024$, $3125$, $7776$, $16 \, 807$, $32 \, 768$, $59 \, 049$, $100 \, 000$, $161 \, 051$, $248 \, 832$:
::$371 \, 293 = 13 \times 13 \times 13 \times 13 \times 13$
:The $5$th power of $13$ after $(1)$, $13$, $169$, $2197$, $28 \, 561$:
::$371 \, 293 = 13^5$
== Also see ==
* 
* 
Category:Specific Numbers
Category:371,293
372

== Number ==
$372$ (three hundred and seventy-two) is:
:$2^2 \times 3 \times 31$
:The $8$th hexagonal pyramidal number after $1$, $7$, $22$, $50$, $95$, $161$, $252$:
::$\ds 372 = \sum_{k \mathop = 1}^8 k \paren {2 k - 1} = \dfrac {8 \paren {8 + 1} \paren {4 \times 8 - 1} } 6$
:The $17$th inconsummate number after $62$, $63$, $65$, $75$, $84$, $95$, $161$, $173$, $195$, $216$, $261$, $266$, $272$, $276$, $326$, $371$:
::$\nexists n \in \Z_{>0}: n = 372 \times \map {s_{10} } n$
:The $30$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $262$, $268$, $276$, $288$, $290$, $292$, $304$, $306$, $322$, $324$, $326$, $336$, $342$
:The $38$th noncototient after $10$, $26$, $34$, $50$, $\ldots$, $290$, $292$, $298$, $310$, $326$, $340$, $344$, $346$, $362$, $366$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 372$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The product with its reversal equals the product of another $3$-digit number with its reversal:
::$372 \times 273 = 651 \times 156$
== Also see ==
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Category:Specific Numbers
Category:372
3721

== Number ==
$3721$ (three thousand, seven hundred and twenty-one) is:
:$61^2$
:The $61$st square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $3249$, $3364$, $3481$, $3600$:
::$3721 = 61 \times 61$
== Also see ==
* 
Category:Specific Numbers
Category:3721
373

== Number ==
$373$ (three hundred and seventy-three) is:
:The $74$th prime number
:The $7$th obstinate number after $1$, $127$, $149$, $251$, $331$, $337$
:The $8$th balanced prime after $5$, $53$, $157$, $173$, $211$, $257$, $263$:
::$373 = \dfrac {367 + 379} 2$
:The $11$th two-sided prime after $2$, $3$, $5$, $7$, $23$, $37$, $53$, $73$, $313$, $317$:
::$373$ is prime; $37$, $3$ are prime; $73$, $3$ are prime
:The $13$th palindromic prime:
::$2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $191$, $313$, $353$, $373$, $\ldots$
:The $19$th permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$, $113$, $131$, $199$, $311$, $337$
:The $19$th near-repdigit prime after $101$, $113$, $131$, $151$, $181$, $191$, $199$, $211$, $223$, $227$, $229$, $233$, $277$, $311$, $313$, $331$, $337$, $353$
:The $20$th right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $29$, $31$, $37$, $53$, $59$, $71$, $73$, $79$, $233$, $239$, $293$, $311$, $313$, $317$
:The $29$th left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $197$, $223$, $283$, $313$, $317$, $337$, $347$, $353$, $367$
== Also see ==
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Category:Specific Numbers
Category:373
374

== Number ==
$374$ (three hundred and seventy-four) is:
:$2 \times 11 \times 17$
:The $41$st sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$, $357$, $366$, $370$:
::$374 = 2 \times 11 \times 17$
== Sources ==
* 
Category:Specific Numbers
Category:374
374, 144,419, 156,711, 147,060, 143,317, 175,368, 453,031, 918,731, 001,856

== Number ==
$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856$ is:
:$2^{168}$
:The $42$nd power of $16$:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 16^{42}$
:The $56$th power of $8$:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 8^{56}$
:The $84$th power of $4$:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 4^{84}$
:The $168$th power of $2$:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 2^{168}$
:The $2 \, 097 \, 152$nd $8$th power:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 2 \, 097 \, 152^8$
:The $16 \, 777 \, 216$th $7$th power:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 16 \, 777 \, 216^7$
:The $268 \, 435 \, 456$th $6$th power:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 268 \, 435 \, 456^6$
:The $4 \, 398 \, 046 \, 511 \, 104$th fourth power:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 4 \, 398 \, 046 \, 511 \, 104^4$
:The $72 \, 057 \, 594 \, 037 \, 927 \, 936$th cube number:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 72 \, 057 \, 594 \, 037 \, 927 \, 936^3$
:The $19 \, 342 \, 813 \, 113 \, 834 \, 066 \, 795 \, 298 \, 816$th square number:
::$374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856 = 19 \, 342 \, 813 \, 113 \, 834 \, 066 \, 795 \, 298 \, 816^2$
:A large power of $2$ which contains no instance of the digit $2$
== Also see ==
* Power of 2 containing no Digit 2
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== Sources ==
* : $374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856$
Category:Specific Numbers
Category:374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856
3741

== Number ==
$3741$ (three thousand, seven hundred and forty-one) is:
:$3 \times 27 \times 43$
:The $86$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $3240$, $3321$, $3403$, $3486$, $3570$, $3655$:
::$3741 = \ds \sum_{k \mathop = 1}^{86} k = \dfrac {86 \times \paren {86 + 1} } 2$
:The $2$nd of the $6$th pair of triangular numbers whose sum and difference are also both triangular:
::$2145 = T_{65}$, $3741 = T_{86}$, $3741 + 2145 = T_{108}$, $3741 - 2145 = T_{56}$
== Also see ==
* 
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Category:Specific Numbers
Category:3741
3744

== Number ==
$3744$ (three thousand, seven hundred and forty-four) is:
:$2^5 \times 3 \times 39$
:The $39$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $\ldots$, $2205$, $2356$, $2512$, $2673$, $2839$, $3010$, $3186$, $3367$, $3553$:
::$3744 = \ds \sum_{k \mathop = 1}^{39} \paren {5 k - 4} = \dfrac {39 \paren {5 \times 39 - 3} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:3744
375

== Number ==
$375$ (three hundred and seventy-five) is:
:$3 \times 5^3$
:The $16$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $24$, $25$, $49$, $51$, $75$, $76$, $99$, $125$, $249$, $251$:
::$375^3 = 52 \, 734 \, \mathbf {375}$
== Also see ==
* 
Category:Specific Numbers
Category:375
3751

== Number ==
$3751$ (three thousand, seven hundred and fifty-one) is:
:$11^2 \times 31$
:The $17$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$, $1541$, $1729$, $1891$, $2465$, $2665$, $2701$, $2821$, $3281$, $3367$:
::$3^{3751} \equiv 3 \pmod {3751}$
:The $27$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $\ldots$, $501$, $624$, $625$, $749$, $751$, $875$, $999$, $1249$:
::$3751^3 = 52 \, 776 \, 57 \mathbf {3 \, 751}$
== Also see ==
* 
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Category:Specific Numbers
Category:3751
376

== Number ==
$376$ (three hundred and seventy-six) is:
:$2^3 \times 47$
:The $6$th automorphic number after $1$, $5$, $6$, $25$, $76$:
::$376^2 = 141 \, \mathbf {376}$
:The $16$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$, $145$, $176$, $210$, $247$, $287$, $330$:
::$376 = \ds \sum_{k \mathop = 1}^{16} \paren {3 k - 2} = \dfrac {16 \paren {3 \times 16 - 1} } 2$
:The $17$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $24$, $25$, $49$, $51$, $75$, $76$, $99$, $125$, $249$, $251$, $375$:
::$376^3 = 53 \, 157 \, \mathbf {376}$
:The $31$st generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $222$, $247$, $260$, $287$, $301$, $330$, $345$:
::$376 = \dfrac {16 \paren {3 \times 16 - 1} } 2$
== Also see ==
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Category:Specific Numbers
Category:376
376,736

== Number ==
$376 \, 736$ (three hundred and seventy-six thousand, seven hundred and thirty-six) is:
:$2^5 \times 61 \times 193$
:The $17$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:376,736
377

== Number ==
$377$ (three hundred and seventy-seven) is:
:$13 \times 29$
:The $6$th after $4$, $13$, $38$, $87$, $208$ in the sequence formed by adding the squares of the first $n$ primes:
::$377 = \ds \sum_{i \mathop = 1}^6 {p_i}^2 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2$
:The $14$th Fibonacci number, after $1$, $1$, $2$, $3$, $5$, $8$, $13$, $21$, $34$, $55$, $89$, $144$, $233$:
::$377 = 144 + 233$
:The $18$th inconsummate number after $62$, $63$, $65$, $75$, $84$, $95$, $161$, $173$, $195$, $216$, $261$, $266$, $272$, $276$, $326$, $371$, $372$:
::$\nexists n \in \Z_{>0}: n = 377 \times \map {s_{10} } n$
== Also see ==
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Category:Specific Numbers
Category:377
378

== Number ==
$378$ (three hundred and seventy-eight) is:
:$2 \times 3^3 \times 7$
:The first of the $3$rd pair of triangular numbers whose sum and difference are also both triangular:
::$378 = T_{27}$, $703 = T_{37}$, $378 + 703 = T_{46}$, $703 - 378 = T_{25}$
:The total of all the entries in a magic cube of order $3$, after $1$, $(36)$:
::$378 = \ds \sum_{k \mathop = 1}^{3^3} k = \dfrac {3^3 \paren {3^3 + 1} } 2$
:The $14$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$, $190$, $231$, $276$, $325$:
::$378 = \ds \sum_{k \mathop = 1}^{14} \paren {4 k - 3} = 14 \paren {2 \times 14 - 1}$
:The $15$th Smith number after $4$, $22$, $27$, $58$, $85$, $94$, $121$, $166$, $202$, $265$, $274$, $319$, $346$, $355$:
::$3 + 7 + 8 = 2 + 3 + 3 + 3 + 7 = 18$
:The $27$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $171$, $190$, $210$, $231$, $253$, $276$, $300$, $325$, $351$:
::$378 = \ds \sum_{k \mathop = 1}^{27} k = \dfrac {27 \times \paren {27 + 1} } 2$
== Also see ==
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Category:Specific Numbers
Category:378
3781

== Number ==
$3781$ (three thousand, seven hundred and eighty-one) is:
:$19 \times 199$
:The $36$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $\ldots$, $2791$, $2977$, $3169$, $3367$, $3571$:
::$3781 = \ds 1 + \sum_{k \mathop = 1}^{36 - 1} 6 k = 36^3 - 35^3$
== Also see ==
* 
Category:Specific Numbers
Category:3781
379

== Number ==
$379$ (three hundred and seventy-nine) is:
:The $75$th prime number
:The $7$th prime $p$ such that $p \# + 1$, where $p \#$ denotes primorial (product of all primes up to $p$) of $p$, is prime:
::$2$, $3$, $5$, $7$, $11$, $31$, $379$
:The $13$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$
:The $21$st right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $29$, $31$, $37$, $53$, $59$, $71$, $73$, $79$, $233$, $239$, $293$, $311$, $313$, $317$, $373$
:The $27$th long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $181$, $193$, $223$, $229$, $233$, $257$, $263$, $269$, $313$, $337$, $367$
== Also see ==
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Category:Specific Numbers
Category:379
3795

== Number ==
$3795$ (three thousand, seven hundred and ninety-five) is:
:$3 \times 5 \times 11 \times 23$
:The $22$nd square pyramidal number after $1$, $5$, $14$, $30$, $55$, $\ldots$, $1015$, $1240$, $1496$, $1785$, $2109$, $2470$, $2870$, $3311$:
::$3795 = \ds \sum_{k \mathop = 1}^{22} k^2 = \dfrac {22 \paren {22 + 1} \paren {2 \times 22 + 1} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:3795
3797

== Number ==
$3797$ (three thousand, seven hundred and ninety-seven) is:
:The $528$th prime number
:The $14$th two-sided prime after $2$, $3$, $5$, $7$, $23$, $37$, $53$, $73$, $313$, $317$, $373$, $797$, $3137$:
::$3797$ is two-sided prime; $379$, $37$, $3$ are prime; $797$, $97$, $7$ are prime
== Also see ==
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Category:Specific Numbers
Category:3797
37 is Second Number whose Period of Reciprocal is 3

== Theorem ==
$37$ is the $2$nd positive integer (after $27$) the decimal expansion of whose reciprocal has a period of $3$:
:$\dfrac 1 {37} = 0 \cdotp \dot 02 \dot 7$
== Proof ==
From Reciprocal of $37$:
Counting the digits, it is seen that this has a period of recurrence of $3$.
It can be determined by inspection of all smaller integers that this is indeed the $2$nd to have a period of $3$.
== Sources ==
* : $27$
* : $999$
* : $37$
* : $999$
Category:37
Category:Examples of Reciprocals
38

== Number ==
$38$ (thirty-eight) is:
:$2 \times 19$
:The magic constant of the order 3 magic hexagon.
:The common sum of the $1$st triplet of consecutive positive even integers $n$ with the property $n + \map {\sigma_0} n = m$ for some $m$:
::$38 = 30 + \map {\sigma_0} {30} = 32 + \map {\sigma_0} {32} = 34 + \map {\sigma_0} {34}$
:The $1$st positive integer whose square ends in $444$:
::$38^2 = 1444$
:The $3$rd after $4$, $13$ in the sequence formed by adding the squares of the first $n$ primes:
::$38 = \ds \sum_{i \mathop = 1}^3 {p_i}^2 = 2^2 + 3^2 + 5^2$
:The $4$th nontotient after $14$, $26$, $34$:
::$\nexists m \in \Z_{>0}: \map \phi m = 38$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $5$th integer after $7$, $13$, $19$, $35$ the decimal representation of whose square can be split into two parts which are each themselves square:
::$38^2 = 1444$; $144 = 12^2$, $4 = 2^2$
:The $10$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$
:The $14$th semiprime after $4$, $6$, $9$, $10$, $14$, $15$, $21$, $22$, $25$, $26$, $33$, $34$, $35$:
::$38 = 2 \times 19$
:The $14$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$, $16$, $18$, $26$, $28$, $36$:
::$36 = 2 + 36$
:The $14$th and largest even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$, $16$, $20$, $22$, $26$, $28$, $32$ which cannot be expressed as the sum of $2$ composite odd numbers.
:The $15$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
::$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $\ldots$
:The $24$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $26$, $29$, $30$, $31$, $32$, $33$, $37$ which cannot be expressed as the sum of distinct pentagonal numbers.
:The $28$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $27$, $30$, $31$, $32$, $35$, $36$, $37$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
== Also see ==
* Magic Constant of Order 3 Magic Hexagon
* Smallest Consecutive Even Numbers such that Added to Divisor Count are Equal
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* 
* 
* 
== Sources ==
* : $38$
* : $38$
Category:Specific Numbers
Category:38
38,416

== Number ==
$38 \, 416$ (thirty-eight thousand, four hundred and sixteen) is:
:$2^4 \times 7^4$
:The $4$th power of $14$ after $(1)$, $14$, $196$, $2744$:
::$38 \, 416 = 14^4$
:The $14$th fourth power after $1$, $16$, $81$, $256$, $625$, $1296$, $2401$, $4096$, $6561$, $10 \, 000$, $14 \, 641$, $20 \, 736$, $28 \, 561$:
::$38 \, 416 = 14 \times 14 \times 14 \times 14$
:The $196$th square number:
::$38 \, 416 = 196 \times 196$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:38,416
380

== Number ==
$380$ (three hundred and eighty) is:
:$2^2 \times 5 \times 19$
:The $19$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$, $125$, $130$, $190$, $205$, $223$, $253$, $285$, $305$, $350$ the decimal representation of whose square can be split into two parts which are each themselves square:
::$380^2 = 144 \, 400$; $144 = 12^2$, $400 = 20^2$
== Also see ==
* 
Category:Specific Numbers
Category:380
381

== Number ==
$381$ (three hundred and eighty-one) is:
:$3 \times 127$
:The $8$th positive integer after $1$, $7$, $102$, $110$, $142$, $159$, $187$ the sum of whose divisors is a cube:
::$\map {\sigma_1} {381} = 512 = 8^3$
:The $19$th inconsummate number after $62$, $63$, $65$, $75$, $84$, $95$, $161$, $173$, $195$, $216$, $261$, $266$, $272$, $276$, $326$, $371$, $372$, $377$:
::$\nexists n \in \Z_{>0}: n = 381 \times \map {s_{10} } n$
== Sources ==
* 
* 
Category:Specific Numbers
Category:381
381,028

== Number ==
$381 \, 028$ (three hundred and eighty-one thousand and twenty-eight) is:
:$2^2 \times 95 \, 257$
:The $18$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:381,028
381,654,729

== Number ==
$381 \, 654 \, 729$ is:
:$3^2 \times 19 \times 557 \times 4007$
:The only polydivisible number which is pandigital in the sense of excluding zero
== Also see ==
* Pandigital Polydivisible Number excluding Zero
== Sources ==
* : $381,654,729$
Category:Specific Numbers
Category:381,654,729
3816

== Number ==
$3816$ (three thousand, eight hundred and sixteen) is:
:$2^3 \times 3^2 \times 53$
:The $36$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $2296$, $2465$, $2640$, $2821$, $3008$, $3201$, $3400$, $3605$:
::$3816 = \ds \sum_{k \mathop = 1}^{36} \paren {6 k - 5} = 36 \paren {3 \times 36 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:3816
382

== Number ==
$382$ (three hundred and eighty-two) is:
:$2 \times 191$
:The $16$th Smith number after $4$, $22$, $27$, $58$, $85$, $94$, $121$, $166$, $202$, $265$, $274$, $319$, $346$, $355$, $378$:
::$3 + 8 + 2 = 2 + 1 + 9 + 1 = 13$
:The $22$nd number whose divisor sum is square:
:
== Also see ==
* 
* 
Category:Specific Numbers
Category:382
3828

== Number ==
$3828$ (three thousand, eight hundred and twenty-eight) is:
:$2^2 \times 3 \times 11 \times 29$
:The $44$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $2145$, $2278$, $2415$, $2556$, $2701$, $2850$, $3003$, $3160$, $3321$, $3486$, $3655$:
::$3828 = \ds \sum_{k \mathop = 1}^{44} \paren {4 k - 3} = 44 \paren {2 \times 44 - 1}$
:The $87$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $3240$, $3321$, $3403$, $3486$, $3570$, $3655$, $3741$:
::$3828 = \ds \sum_{k \mathop = 1}^{87} k = \dfrac {87 \times \paren {87 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:3828