nyuuzyou/wikis huggingface dataset:
735

== Number ==
$735$ (seven hundred and thirty-five) is:
:$3 \times 5 \times 7^2$
:The $33$rd Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $216$, $224$, $312$, $315$, $384$, $432$, $612$, $624$, $672$:
::$735 = 7 \times 105 = 7 \times \paren {7 \times 3 \times 5}$
== Also see ==
* 
== Sources ==
* : $735$
Category:Specific Numbers
Category:735
736

== Number ==
$736$ (seven hundred and thirty-six) is:
:$2^5 \times 23$
:The $16$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $96$, $133$, $176$, $225$, $280$, $341$, $408$, $481$, $560$, $645$:
::$736 = \ds \sum_{k \mathop = 1}^{16} \paren {6 k - 5} = 16 \paren {3 \times 16 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:736
737

== Number ==
$737$ (seven hundred and thirty-seven) is:
:$11 \times 67$
:The $22$nd second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $222$, $260$, $301$, $345$, $392$, $442$, $495$, $551$, $610$, $672$:
::$737 = \dfrac {22 \paren {3 \times 22 + 1} } 2$
:The $44$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$, $651$, $672$, $715$:
::$737 = \dfrac {22 \paren {3 \times 22 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:737
7381

== Number ==
$7381$ (seven thousand, three hundred and eighty-one) is:
:$11^2 \times 61$
:The total of all the entries in a magic square of order $11$, after $1$, $(10)$, $45$, $136$, $325$, $666$, $1225$, $2080$, $3321$, $5050$:
::$7381 = \ds \sum_{k \mathop = 1}^{11^2} k = \dfrac {11^2 \paren {11^2 + 1} } 2$
:The $61$st hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $5565$, $5778$, $5995$, $6216$, $6441$, $6670$, $6903$, $7140$:
::$7381 = \ds \sum_{k \mathop = 1}^{61} \paren {4 k - 3} = 61 \paren {2 \times 61 - 1}$
:The $121$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $6786$, $6903$, $7021$, $7140$, $7260$:
::$7381 = \ds \sum_{k \mathop = 1}^{121} k = \dfrac {121 \times \paren {121 + 1} } 2$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:7381
739

== Number ==
$739$ (seven hundred and thirty-nine) is:
:The $131$st prime number
:The $24$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $311$, $337$, $347$, $359$, $389$, $709$, $733$
:The $26$th right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $\ldots$, $317$, $373$, $379$, $593$, $599$, $719$, $733$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:739
739,397

== Number ==
$739 \, 397$ (seven hundred and thirty-nine thousand, three hundred and ninety-seven) is:
:The $59 \, 489$th prime number
:The $15$th and last two-sided prime after $2$, $3$, $5$, $7$, $23$, $37$, $53$, $73$, $313$, $317$, $373$, $797$, $3137$, $3797$:
::$739 \, 397$ is prime; $73 \, 939$, $7393$, $739$, $73$, $7$ are prime; $39 \, 397$, $9397$, $397$, $97$, $7$ are prime
== Also see ==
* 
* 
== Sources ==
* : $739,397$
* : $739,397$
Category:Specific Numbers
Category:739,397
7396

== Number ==
$7396$ (seven thousand, three hundred and ninety-six) is:
:$2^2 \times 43^2$
:The $86$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $6084$, $6241$, $6400$, $6561$, $6724$, $6889$, $7056$, $7225$
::$7396 = 86 \times 86$
== Also see ==
* 
Category:Specific Numbers
Category:7396
73 is Smallest Number whose Period of Reciprocal is 8

== Theorem ==
$73$ is the first positive integer the decimal expansion of whose reciprocal has a period of $8$:
:$\dfrac 1 {73} = 0 \cdotp \dot 01369 \, 86 \dot 3$
== Proof ==
From Reciprocal of $73$:
Counting the digits, it is seen that this has a period of recurrence of $8$.
It remains to be shown that $73$ is the smallest positive integer which has this property.
Category:73
Category:Examples of Reciprocals
74

== Number ==
$74$ (seventy-four) is:
:$2 \times 37$
:The $1$st element of the $1$st pair of consecutive even nontotients.
:The $2$nd of the $2$nd ordered quadruple of consecutive integers that have divisor sums which are strictly increasing:
::$\map {\sigma_1} {73} = 74$, $\map {\sigma_1} {74} = 114$, $\map {\sigma_1} {75} = 124$, $\map {\sigma_1} {76} = 140$
:The $6$th integer $n$ after $-1$, $0$, $2$, $7$, $15$ such that $\dbinom n 0 + \dbinom n 1 + \dbinom n 2 + \dbinom n 3 = m^2$ for integer $m$:
::$\dbinom {74} 0 + \dbinom {74} 1 + \dbinom {74} 2 + \dbinom {74} 3 = 260^2$
:The $8$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$:
::$\nexists m \in \Z_{>0}: \map \phi m = 74$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $25$th semiprime:
::$74 = 2 \times 37$
:The $28$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
::$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $68$, $69$, $74$, $\ldots$
== Also see ==
* Smallest Consecutive Even Nontotients
* 
* 
* 
* 
* 
== Sources ==
* : $74$
Category:Specific Numbers
Category:74
74,162

== Number ==
$74 \, 162$ (seventy-four thousand, one hundred and sixty-two) is:
:$2 \times 11 \times 3371$
:Has the property that the digits of its square occur in $5$ adjacent pairs:
::$74 \, 162^2 = 5 \, 500 \, 002 \, 244$
== Also see ==
* Squares whose Digits appear in Pairs
== Sources ==
* 
* 
* : $74,162$
Category:Specific Numbers
Category:74,162
74,162/Mistake

== Source Work ==
:
:The Dictionary
::$74,162$
== Mistake ==
:$74,162^2 = 5,500,002,244$ [ v17 84]
== Correction ==
The referenced page $84$ of actually contains an article on tic-tac-toe.
The question was raised on page $59$ of volume $16$ issue $1$ by of Cheroy, France, in the Problems and Conjectures column.
He asks for a square of the form $a_1 a_1 a_2 a_2 \dots a_n a_n$, citing $88^2 = 7744$ as an example.
He also asks whether there are infinite number of such numbers.
In , volume $17$ issue $1$ on page $70$, of Hapton, Middlesex, England gives the solution $74 \, 162$.
 states that there are no more solutions under $10^8$, conjecturing that there are only a finite number of them.
== Sources ==
* : $74,162$
Category:Mistakes/Curious and Interesting Numbers
74,943

== Number ==
$74 \, 943$ (seventy-four thousand, nine hundred and forty-three) is:
:$3^2 \times 11 \times 757$
:One of the elements of one of the $4$-cycles to which Kaprekar's process on some $5$-digit numbers converges:
::$74 \, 943 \to 62 \, 964 \to 71 \, 973 \to 83 \, 952 \to 74 \, 943$
== Also see ==
* 
Category:Specific Numbers
Category:74,943
7400

== Number ==
$7400$ (seven thousand, four hundred) is:
:$2^3 \times 5^2 \times 37$
:The $50$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $5985$, $6256$, $6533$, $6816$, $7105$:
::$7400 = \ds \sum_{k \mathop = 1}^{50} \paren {6 k - 5} = 50 \paren {3 \times 50 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:7400
741

== Number ==
$741$ (seven hundred and forty-one) is:
:$3 \times 13 \times 19$
:The $38$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $325$, $351$, $378$, $406$, $435$, $465$, $496$, $528$, $561$, $595$, $630$, $666$, $703$:
::$741 = \ds \sum_{k \mathop = 1}^{38} k = \dfrac {38 \times \paren {38 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:741
742

== Number ==
$742$ (seven hundred and forty-two) is:
:$2 \times 7 \times 53$
:The $8$th Keith number after $14$, $19$, $28$, $47$, $61$, $75$, $197$:
::$7$, $4$, $2$, $13$, $19$, $34$, $66$, $119$, $219$, $404$, $742$, $\ldots$
:The $34$th number whose divisor sum is square:
::$\map {\sigma_1} {742} = 1296 = 36^2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:742
742,900

== Number ==
$742 \, 900$ (seven hundred and forty-two thousand, nine hundred) is:
:$2^2 \times 5^2 \times 17 \times 19 \times 23$
:The $13$th Catalan number after $(1)$, $1$, $2$, $5$, $14$, $42$, $132$, $429$, $1430$, $4862$, $16 \, 796$, $58 \, 786$, $208 \, 012$:
::$742 \, 900 = \dfrac 1 {13 + 1} \dbinom {2 \times 13} {13} = \dfrac 1 {14} \times 10 \, 400 \, 600$
== Also see ==
* 
Category:Specific Numbers
Category:742,900
7425

== Number ==
$7425$ (seven thousand, four hundred and twenty-five) is:
:$3^3 \times 5^2 \times 11$
:The $15$th odd abundant number after $945$, $1575$, $2205$, $2835$, $3465$, $4095$, $4725$, $5355$, $5775$, $5985$, $6435$, $6615$, $6825$, $7245$:
::$\map {\sigma_1} {7425} - 7425 = 7455 > 7425$
== Also see ==
* 
Category:Specific Numbers
Category:7425
743

== Number ==
$743$ (seven hundred and forty-three) is:
:The $132$nd prime number.
:The smaller of the $11$th pair of primes whose prime gap is $8$:
::$751 - 743 = 8$
:The $25$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $311$, $337$, $347$, $359$, $389$, $709$, $733$, $739$
:The $33$rd Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $233$, $239$, $251$, $281$, $293$, $359$, $419$, $431$, $443$, $491$, $509$, $593$, $641$, $653$, $659$, $683$, $719$:
::$2 \times 743 + 1 = 1487$, which is prime.
:The $43$rd left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $443$, $467$, $523$, $547$, $613$, $617$, $643$, $647$, $653$, $673$, $683$
:The $48$th long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $491$, $499$, $503$, $509$, $541$, $571$, $577$, $593$, $619$, $647$, $659$, $701$, $709$, $727$
== Also see ==
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:743
7447

== Number ==
$7447$ (seven thousand, four hundred and forty-seven) is:
:$11 \times 677$
:The $12$th integer after $0$, $1$, $3$, $5$, $7$, $9$, $33$, $99$, $313$, $585$, $717$ which is palindromic in both decimal and binary:
::$7447_{10} = 1 \, 110 \, 100 \, 010 \, 111_2$
== Also see ==
* 
Category:Specific Numbers
Category:7447
748

== Number ==
$748$ (seven hundred and forty-eight) is:
:$2^2 \times 11 \times 17$
:The $12$th primitive abundant number after $20$, $70$, $88$, $104$, $272$, $304$, $368$, $464$, $550$, $572$, $650$:
::$1 + 2 + 4 + 11 + 17 + 22 + 34 + 44 + 68 + 187 + 374 = 764 > 748$
:The $16$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $272$, $304$, $350$, $368$, $464$, $490$, $496$, $550$, $572$, $650$:
::$748 = 2 + 17 + 22 + 34 + 44 + 68 + 187 + 374$
== Also see ==
* 
* 
Category:Specific Numbers
Category:748
749

== Number ==
$749$ (seven hundred and forty-nine) is:
:$7 \times 107$
:The $22$nd trimorphic number after $1$, $4$, $5$, $6$, $9$, $\ldots$, $375$, $376$, $499$, $501$, $624$, $625$:
::$749^3 = 420 \, 189 \, \mathbf {749}$
== Also see ==
* 
Category:Specific Numbers
Category:749
75

== Number ==
$75$ (seventy-five) is:
:$3 \times 5^2$
:With $48$, an element of the $1$st quasiamicable pair:
::$\map {\sigma_1} {48} = \map {\sigma_1} {75} = 124 = 48 + 75 + 1$
:The $1$st of the $2$nd pair of consecutive integers which both have $6$ divisors:
::$\map {\sigma_0} {75} = \map {\sigma_0} {76} = 6$
:The $3$rd of the $2$nd ordered quadruple of consecutive integers that have divisor sums which are strictly increasing:
::$\map {\sigma_1} {73} = 74$, $\map {\sigma_1} {74} = 114$, $\map {\sigma_1} {75} = 124$, $\map {\sigma_1} {76} = 140$
:The $4$th inconsummate number after $62$, $63$, $65$:
::$\nexists n \in \Z_{>0}: n = 75 \times \map {s_{10} } n$
:The $5$th pentagonal pyramidal number after $1$, $6$, $12$, $40$:
::$75 = 1 + 5 + 12 + 22 + 35 = \dfrac {5^2 \paren {5 + 1} } 2$
:The $5$th tri-automorphic number after $2$, $5$, $7$, $67$:
::$75^2 \times 3 = 16 \, 8 \mathbf {75}$
:The index (after $2$, $3$, $6$, $30$) of the $5$th Woodall prime:
::$75 \times 2^{75} - 1$
:The $6$th Keith number after $14$, $19$, $28$, $47$, $61$:
::$7$, $5$, $12$, $17$, $29$, $46$, $75$, $\ldots$
:The $6$th positive integer $n$ after $4$, $7$, $15$, $21$, $45$ such that $n - 2^k$ is prime for all $k$
:The $10$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $24$, $25$, $49$, $51$:
::$75^3 = 421 \, 8 \mathbf {75}$
:The $18$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $\ldots$
:The $29$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
::$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $68$, $69$, $74$, $75$, $\ldots$
== Also see ==
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:75
75,933

== Number ==
$75 \, 933$ (seventy-five thousand, nine hundred and thirty-three) is:
:$3^2 \times 11 \times 13 \times 59$
:One of the elements of one of the $4$-cycles to which Kaprekar's process on some $5$-digit numbers converges:
::$75 \, 933 \to 63 \, 954 \to 61 \, 974 \to 82 \, 962 \to 75 \, 933$
== Also see ==
* 
Category:Specific Numbers
Category:75,933
7503

== Number ==
$7503$ (seven thousand, five hundred and three) is:
:$3 \times 41 \times 61$
:The $122$nd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $6786$, $6903$, $7021$, $7140$, $7260$, $7381$:
::$7503 = \ds \sum_{k \mathop = 1}^{122} k = \dfrac {122 \times \paren {122 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:7503
751

== Number ==
$751$ (seven hundred and fifty-one) is:
:The $133$rd prime number
:The larger of the $11$th pair of primes whose prime gap is $8$:
::$751 - 743 = 8$
:The index (after $2$, $3$, $6$, $30$, $75$, $81$, $115$, $123$, $249$, $362$, $384$, $462$, $512$) of the $14$th Woodall prime:
::$751 \times 2^{751} - 1$
:The $20$th of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 19^2 + 29 = 751$ ()
:The $23$rd trimorphic number after $1$, $4$, $5$, $6$, $9$, $\ldots$, $375$, $376$, $499$, $501$, $624$, $625$, $749$:
::$751^3 = 423 \, 563 \, \mathbf {751}$
:The $25$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $311$, $337$, $347$, $359$, $389$, $709$, $733$, $739$, $743$
== Also see ==
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:751
754,788,753,590,897

== Number ==
$754 \, 788 \, 753 \, 590 \, 897$ is:
:$23 \times 32 \, 816 \, 902 \, 330 \, 039$
:The $55$th Keith number
== Also see ==
* 
== Sources ==
* : $754,788,753,590,897$
Category:Specific Numbers
Category:754,788,753,590,897
756

== Number ==
$504$ (seven hundred and fifty-six) is:
: $2^2 \times 3^3 \times 7$
:The $2$nd positive integer after $504$ which can be expressed as the product of $2$ two-digit numbers in $2$ ways such that the factors in one of those pairs is the reversal of each of the factors in the other:
::$756 = 12 \times 63 = 36 \times 21$
== Also see ==
* 
Category:Specific Numbers
Category:756
756,839

== Number ==
$756 \, 839$ (seven hundred and fifty-six thousand, eight hundred and thirty-nine) is:
:The $60 \, 745$th prime number
:The index of the $32$nd Mersenne prime after $2$, $3$, $5$, $7$, $13$, $\ldots$, $11 \, 213$, $19 \, 937$, $21 \, 701$, $23 \, 209$, $44 \, 497$, $86 \, 243$, $110 \, 503$, $132 \, 049$, $216 \, 091$:
::$M_{756 \, 839} = 2^{756 \, 839} - 1 \approx 1 \cdotp 741 \times 10^{227 \, 831}$
== Also see ==
* 
* 
== Historical Note ==
== Sources ==
* : $2^{859,433} - 1$
Category:Specific Numbers
Category:756,839
7560

== Number ==
$7560$ (seven thousand, five hundred and sixty) is:
:$2^3 \times 3^3 \times 5 \times 7$
:The $1$st highly composite number which is not also superabundant:
::$\dfrac {\map {\sigma_1} {7560} } {7560} = \dfrac {28 \, 800} {7560} \approx 3 \cdotp 810$, but $\dfrac {\map {\sigma_1} {5040} } {5040} = \dfrac {19 \, 344} {5040} \approx 3 \cdotp 838$, which is greater
:The $20$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$, $2520$, $5040$:
::$\map {\sigma_0} {7560} = 64$
== Also see ==
* 
== Sources ==
* : $7560$
* : $7560$
Category:Specific Numbers
Category:7560
7569

== Number ==
$7569$ (seven thousand, five hundred and sixty-nine) is:
:$3^2 \times 29^2$
:The $87$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $6084$, $6241$, $6400$, $6561$, $6724$, $6889$, $7056$, $7225$, $7396$
::$7569 = 87 \times 87$
== Also see ==
* 
Category:Specific Numbers
Category:7569
757

== Number ==
$757$ (seven hundred and fifty-seven) is:
:The $134$th prime number
:The $11$th obstinate number after $1$, $127$, $149$, $251$, $331$, $337$, $373$, $509$, $599$, $701$
:The $16$th palindromic prime:
::$2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $191$, $313$, $353$, $373$, $383$, $727$, $757$, $\ldots$
:The $32$nd near-repdigit prime after $101$, $113$, $131$, $151$, $\ldots$, $353$, $373$, $383$, $433$, $443$, $449$, $499$, $557$, $577$, $599$, $661$, $677$, $727$, $733$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:757
758,083,947,856,951

== Number ==
$758 \, 083 \, 947 \, 856 \, 951$ is:
:A prime number
:The $1$st term of the smallest Cunningham chain of the second kind of length $13$:
::$758 \, 083 \, 947 \, 856 \, 951$, $1 \, 516 \, 167 \, 895 \, 713 \, 901$, $3 \, 032 \, 335 \, 791 \, 427 \, 801$, $6 \, 064 \, 671 \, 582 \, 855 \, 601$, $12 \, 129 \, 343 \, 165 \, 711 \, 201$, $24 \, 258 \, 686 \, 331 \, 422 \, 401$, $48 \, 517 \, 372 \, 662 \, 844 \, 801$, $97 \, 034 \, 745 \, 325 \, 689 \, 601$, $194 \, 069 \, 490 \, 651 \, 379 \, 201$, $388 \, 138 \, 981 \, 302 \, 758 \, 401$, $776 \, 277 \, 962 \, 605 \, 516 \, 801$, $1 \, 552 \, 555 \, 925 \, 211 \, 033 \, 601$, $3 \, 105 \, 111 \, 850 \, 422 \, 067 \, 201$
== Also see ==
* 
* 
== Sources ==
* : $758,083,947,856,951$
Category:Specific Numbers
Category:758,083,947,856,951
759,375

== Number ==
$759 \, 375$ (seven hundred and fifty-nine thousand, three hundred and seventy-five) is:
:$3^5 \times 5^5$
:The $15$th fifth power after $1$, $32$, $243$, $1024$, $3125$, $7776$, $16 \, 807$, $32 \, 768$, $59 \, 049$, $100 \, 000$, $161 \, 051$, $248 \, 832$, $371 \, 293$, $537 \, 824$:
::$759 \, 375 = 15 \times 15 \times 15 \times 15 \times 15$
:The $5$th power of $15$ after $(1)$, $15$, $225$, $3375$, $50 \, 625$:
::$759 \, 375 = 15^5$
== Also see ==
* 
* 
Category:Specific Numbers
Category:759,375
76

== Number ==
$76$ (seventy-six) is:
:$2^2 \times 19$
:The $2$nd element of the $1$st pair of consecutive even nontotients.
:The $2$nd of the $2$nd pair of consecutive integers which both have $6$ divisors:
::$\map {\sigma_0} {75} = \map {\sigma_0} {76} = 6$
:The $4$th of the $2$nd ordered quadruple of consecutive integers that have divisor sums which are strictly increasing:
::$\map {\sigma_1} {73} = 74$, $\map {\sigma_1} {74} = 114$, $\map {\sigma_1} {75} = 124$, $\map {\sigma_1} {76} = 140$
:The $5$th automorphic number after $1$, $5$, $6$, $25$:
::$76^2 = 57 \mathbf {76}$
:The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $7$ different ways
:The $9$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$, $74$:
::$\nexists m \in \Z_{>0}: \map \phi m = 76$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $9$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$, $29$, $47$:
::$76 = 29 + 47$
:The $11$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $24$, $25$, $49$, $51$, $75$:
::$76^3 = 438 \, 9 \mathbf {76}$
:The $26$th positive integer which is not the sum of $1$ or more distinct squares:
::$2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $44$, $47$, $48$, $60$, $67$, $72$, $76$, $\ldots$
:The $33$rd integer $n$ such that $2^n$ contains no zero in its decimal representation:
::$2^{76} = 75 \, 557 \, 863 \, 725 \, 914 \, 323 \, 419 \, 136$
== Also see ==
* Smallest Consecutive Even Nontotients
* 
* 
* 
* 
* 
* 
* 
* 
* 
== Sources ==
* : $76$
* : $76$
Category:Specific Numbers
Category:76
76,182

== Number ==
$76 \, 182$ (seventy-six thousand, one hundred and eighty-two) is:
:$2 \times 3 \times 12 \, 697$
:The larger of the $4$th pandigital pair, with $59 \, 403$, of integers each have squares which are themselves pandigital:
::$59 \, 403^2 = 3 \, 528 \, 716 \, 409$, $76 \, 182^2 = 5 \, 803 \, 697 \, 124$
== Also see ==
* 
== Sources ==
* : $57,321$
Category:Specific Numbers
Category:76,182
76,923

== Number ==
$76 \, 923$ (seventy-six thousand, nine hundred and twenty-three) is:
:$3^3 \times 7 \times 11 \times 37$
:With a zero prepended, its cyclic permutations are multiples of it:
::$076 \, 923 = 1 \times 76 \, 923$
::$307 \, 692 = 4 \times 76 \, 923$
::$230 \, 769 = 3 \times 76 \, 923$
::$923 \, 076 = 12 \times 76 \, 923$
::$692 \, 307 = 9 \times 76 \, 923$
::$769 \, 230 = 10 \times 76 \, 923$
== Also see ==
* Recurring Parts of Multiples of One Thirteenth
== Sources ==
* : $076,923$
* : $076,923$
Category:Specific Numbers
Category:76,923
761

== Number ==
$761$ (seven hundred and sixty-one) is:
:The $135$th prime number.
:The smaller of the $12$th pair of primes whose prime gap is $8$:
::$769 - 761 = 8$
:The $26$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $311$, $337$, $347$, $359$, $389$, $709$, $733$, $739$, $743$, $751$
:The $34$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $431$, $443$, $491$, $509$, $593$, $641$, $653$, $659$, $683$, $719$, $743$:
::$2 \times 761 + 1 = 1523$, which is prime.
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:761
762

== Number ==
$762$ (seven hundred and sixty-two) is:
:$2 \times 3 \times 127$
:The $39$th Smith number after $4$, $22$, $27$, $58$, $\ldots$, $648$, $654$, $663$, $666$, $690$, $706$, $728$, $729$:
::$7 + 6 + 2 = 2 + 3 + 1 + 2 + 7 = 15$
== Also see ==
* 
Category:Specific Numbers
Category:762
7626

== Number ==
$7626$ (seven thousand, six hundred and twenty-six) is:
:$2 \times 3 \times 31 \times 41$
:The $62$nd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $5565$, $5778$, $5995$, $6216$, $6441$, $6670$, $6903$, $7140$, $7381$:
::$7626 = \ds \sum_{k \mathop = 1}^{62} \paren {4 k - 3} = 62 \paren {2 \times 62 - 1}$
:The $123$rd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $6786$, $6903$, $7021$, $7140$, $7260$, $7381$, $7503$:
::$7626 = \ds \sum_{k \mathop = 1}^{123} k = \dfrac {123 \times \paren {123 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:7626
7641

== Number ==
$7641$ (seven thousand, six hundred and forty-one) is:
:$3^3 \times 283$
: The $6$th integer after $954$, $1980$, $2961$, $3870$, $5823$ whose digits are unchanged when subtracting its reversal:
::$7641 - 1467 = 6174$
== Also see ==
* 
Category:Specific Numbers
Category:7641
767

== Number ==
$767$ (seven hundred and sixty-seven) is:
:$13 \times 59$
:The $8$th Thabit number after $(2)$, $5$, $11$, $23$, $47$, $95$, $191$, $383$:
::$767 = 3 \times 2^8 - 1$ 
:The $7$th and last integer $n$ after $-1$, $0$, $2$, $7$, $15$, $74$ such that $\dbinom n 0 + \dbinom n 1 + \dbinom n 2 + \dbinom n 3 = m^2$ for integer $m$:
::$\dbinom {767} 0 + \dbinom {767} 1 + \dbinom {767} 2 + \dbinom {767} 3 = 8672^2$
== Also see ==
* 
* 
== Sources ==
* : $767$
Category:Specific Numbers
Category:767
768

== Number ==
$768$ (seven hundred and sixty-eight) is:
:$2^8 \times 3$
:The $17$th positive integer after $128$, $192$, $256$, $288$, $320$, $384$, $432$, $448$, $480$, $512$, $576$, $640$, $648$, $672$, $704$, $720$ with $7$ or more prime factors:
::$768 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
== Also see ==
* 
Category:Specific Numbers
Category:768
769

== Number ==
$769$ (seven hundred and sixty-nine) is:
:The $136$th prime number.
:The larger of the $12$th pair of primes whose prime gap is $8$:
::$769 - 761 = 8$
:The $16$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$, $113$, $193$, $241$, $257$, $353$, $449$, $577$, $641$, $673$:
::$769 = 3 \times 2^8 + 1$
:The $27$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $311$, $337$, $347$, $359$, $389$, $709$, $733$, $739$, $743$, $751$, $761$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:769