# 114

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## Number

$114$ (one hundred and fourteen) is:

$2 \times 3 \times 19$

The number of different ways to colour the faces of a cube with $3$ given colours, one colour per face.

The $9$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$:
$114 = 2 \times 3 \times 19$

The smallest positive integer which can be expressed as the sum of $2$ odd primes in $10$ ways.

The $14$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$, $74$, $76$, $86$, $90$, $94$, $98$:
$\nexists m \in \Z_{>0}: \map \phi m = 114$
where $\map \phi m$ denotes the Euler $\phi$ function