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