385

Number
$385$ (three hundred and eighty-five) is:


 * $5 \times 7 \times 11$


 * The $3$rd of the $3$-digit integers $m$ which need the largest number of reverse-and-add process iterations ($23$) before reaching a palindromic number:
 * $385$, $968$, $1837$, $\ldots$, $8713200023178$


 * The $7$th Cullen number after $1$, $3$, $9$, $25$, $65$, $161$:
 * $385 = 6 \times 2^6 + 1$


 * The $10$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $91$, $140$, $204$, $285$:
 * $385 = \ds \sum_{k \mathop = 1}^{10} k^2 = \dfrac {10 \paren {10 + 1} \paren {2 \times 10 + 1} } 6$


 * The number of integer partitions for $18$:
 * $\map p {18} = 385$


 * The $19$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$, $85$, $89$, $101$, $125$, $145$, $149$, $245$, $265$, $365$ such that the Fibonacci number $F_n$ ends in $n$


 * The $23$rd number whose divisor sum is square:


 * The $42$nd sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$, $357$, $366$, $370$, $374$:
 * $385 = 5 \times 7 \times 11$