270

Number
$270$ (two hundred and seventy) is:


 * $2 \times 3^3 \times 5$


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


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