76
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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
- Previous ... Next: Lucas Number
- Previous ... Next: Powers of 2 with no Zero in Decimal Representation
- Previous ... Next: Numbers not Sum of Distinct Squares
- Previous ... Next: Nontotient
- Previous ... Next: Pairs of Consecutive Integers with 6 Divisors
- Previous ... Next: Trimorphic Number
- Previous: Sequences of 4 Consecutive Integers with Rising Divisor Sum
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $76$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $76$