165

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 $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$:

$165 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 = \dfrac {9 \paren {9 + 1} \paren {9 + 2} } 6$

The $1$st of the $2$nd ordered triple of consecutive integers after $\tuple {105, 106, 107}$ that have Euler $\phi$ values which are strictly increasing:

$\map \phi {165} = 80$, $\map \phi {166} = 82$, $\map \phi {167} = 166$