# 111

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## Number

$111$ (one hundred and eleven) is:

$3 \times 37$

The magic constant of the smallest prime magic square.

The $3$rd repuint after $1$, $11$

The $4$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 $6$th positive integer after $1$, $2$, $7$, $11$, $101$ whose cube is palindromic:
$111^3 = 1 \, 367 \, 631$

The magic constant of a magic square of order $6$, after $1$, $(5)$, $15$, $34$, $65$:
$111 = \displaystyle \dfrac 1 6 \sum_{k \mathop = 1}^{6^2} k = \dfrac {6 \paren {6^2 + 1} } 2$

The $7$th palindromic lucky number:
$1$, $3$, $7$, $9$, $33$, $99$, $111$, $\ldots$

The $8$th palindromic integer after $0$, $1$, $2$, $3$, $11$, $22$, $101$ whose square is also palindromic integer
$111^2 = 12 \, 321$

The $15$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$:
$111 = 111 \times 1 = 111 \times \paren {1 \times 1 \times 1}$

The $24$th lucky number:
$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $87$, $93$, $99$, $105$, $111$, $\ldots$

The $35$th semiprime:
$111 = 3 \times 37$