# 187

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## Number

$187$ (one hundred and eighty-seven) is:

$11 \times 17$

The $1$st of the $3$-digit integers $m$ which need the largest number of reverse-and-add process iterations ($23$) before reaching a palindromic number:
$187$, $968$, $1837$, $\ldots$, $8713200023178$

The $7$th positive integer after $1$, $7$, $102$, $110$, $142$, $159$ the sum of whose divisors is a cube:
$\map {\sigma_1} {187} = 216 = 6^3$

The $11$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$, $77$, $100$, $126$, $155$:
$187 = \dfrac {11 \paren {3 \times 11 + 1} } 2$

The $22$nd generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$, $77$, $92$, $100$, $117$, $126$, $145$, $155$, $176$:
$187 = \dfrac {11 \paren {3 \times 11 + 1} } 2$