# 135

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## Number

$135$ (one hundred and thirty-five) is:

$3^3 \times 5$

The $29$th lucky number:
$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $105$, $111$, $115$, $127$, $129$, $133$, $135$, $\ldots$

The $20$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$, $111$, $112$, $115$, $128$, $132$:
$135 = 9 \times 15 = 9 \times \left({1 \times 3 \times 5}\right)$

The $12$th number after $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $89$ which is the sum of the increasing powers of its digits taken in order:
$1^1 + 3^2 + 5^3 = 135$

The $6$th of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:
$73$, $91$, $95$, $111$, $117$, $135$, $146$, $148$, $152$, $182$, $190$, $216$, $222$, $228$, $234$, $252$, $270$

The $26$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.