# 286

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## Number

$286$ (two hundred and eighty-six) is:

$2 \times 11 \times 13$

The $2$nd of the $3$-digit integers $m$ which need the largest number of reverse-and-add process iterations ($23$) before reaching a palindromic number:
$286$, $968$, $1837$, $\ldots$, $8713200023178$

The $3$rd Fermat pseudoprime to base $3$ after $91$, $121$:
$3^{286} \equiv 3 \pmod {286}$

The $11$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$, $165$, $220$:
$286 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 = \dfrac {11 \paren {11 + 1} \paren {11 + 2} } 6$

The $11$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $148$, $189$, $235$:
$286 = 1 + 7 + 11 + 16 + 21 + 26 + 31 + 36 + 41 + 46 + 51 = \dfrac {11 \paren {5 \times 11 - 3} } 2$

The $31$st sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $182$, $186$, $190$, $195$, $222$, $230$, $231$, $246$, $255$, $258$, $266$, $273$, $282$, $285$:
$286 = 2 \times 11 \times 13$

The $46$th nontotient:
$\nexists m \in \Z_{>0}: \map \phi m = 286$
where $\map \phi m$ denotes the Euler $\phi$ function