# 252

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## Number

$252$ (two hundred and fifty-two) is:

$2^2 \times 3^2 \times 7$

The $5$th central binomial coefficient after $2$, $6$, $20$, $70$:
$252 = \dbinom {2 \times 5} 5 := \dfrac {10!} {\paren {5!}^2}$

The $7$th hexagonal pyramidal number after $1$, $7$, $22$, $50$, $95$, $161$:
$252 = \ds \sum_{k \mathop = 1}^7 k \paren {2 k - 1} = \dfrac {7 \paren {7 + 1} \paren {4 \times 7 - 1} } 6$

The $16$th of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:
$73$, $91$, $95$, $111$, $117$, $135$, $146$, $148$, $152$, $182$, $190$, $216$, $222$, $228$, $234$, $252$, $270$