77

Number
$77$ (seventy-seven) is:
 * $7 \times 11$


 * The smallest positive integer having a multiplicative persistence of $4$


 * The $6$th palindromic integer after $0$, $1$, $2$, $3$, $11$ which is the index of a palindromic triangular number
 * $T_{77} = 3003$


 * The $7$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$:
 * $77 = \dfrac {7 \left({3 \times 7 + 1}\right)} 2$


 * The $10$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:
 * $0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$


 * The number of integer partitions for $12$:
 * $\map p {12} = 77$


 * The $14$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$:
 * $77 = \dfrac {7 \left({3 \times 7 + 1}\right)} 2$


 * The $26$th semiprime:
 * $77 = 7 \times 11$


 * The $32$nd odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
 * $1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $\ldots$


 * The $34$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{77} = 151 \, 115 \, 727 \, 451 \, 828 \, 646 \, 838 \, 272$


 * The $41$st positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $50$, $54$, $55$, $59$, $60$, $61$, $65$, $66$, $67$, $72$ which cannot be expressed as the sum of distinct pentagonal numbers


 * The $44$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $55$, $60$, $61$, $65$, $66$, $67$, $72$, $73$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$


 * The smallest (positive) integer which requires $5$ syllables to say it in the English language:
 * sev-en-ty-sev-en


 * The largest positive integer which cannot be expressed as the sum of positive integers whose reciprocals add up to $1$

Also see

 * Positive Integers Expressible by Sum of Integers whose Reciprocals Sum to 1