# 270

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## Number

$270$ (two hundred and seventy) is:

$2 \times 3^3 \times 5$

The $5$th Ore number after $1$, $6$, $28$, $140$:
$\dfrac {270 \times \map {\sigma_0} {270} } {\map {\sigma_1} {270} } = 6$
and the $4$th after $1, 6, 140$ whose divisors also have an arithmetic mean which is an integer:
$\dfrac {\map {\sigma_1} {270} } {\map {\sigma_0} {270} } = 45$

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