# 165

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## Number

$165$ (one hundred and sixty-five) is:

$3 \times 5 \times 11$

The $13$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$, $138$, $154$:
$165 = 3 \times 5 \times 11$

The $9$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$:
$165 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 = \dfrac {9 \left({9 + 1}\right) \left({9 + 2}\right)} 6$

The $1$st of the $2$nd ordered triple of consecutive integers after $\left({105, 106, 107}\right)$ that have Euler $\phi$ values which are strictly increasing:
$\phi \left({165}\right) = 80$, $\phi \left({166}\right) = 82$, $\phi \left({167}\right) = 166$