# 166

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## Number

$166$ (one hundred and sixty-six) is:

$2 \times 83$

The $2$nd of the $2$nd ordered triple of consecutive integers after $\tuple {105, 106, 107}$ that have Euler $\phi$ values which are strictly increasing:
$\map \phi {165} = 80$, $\map \phi {166} = 82$, $\map \phi {167} = 166$

The $8$th Smith number after $4$, $22$, $27$, $58$, $85$, $94$, $121$:
$1 + 6 + 6 = 2 + 8 + 3 = 13$

The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $11$ different ways

The $12$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$