161

Number
$161$ (one hundred and sixty-one) is:


 * $7 \times 23$


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


 * The $6$th Cullen number after $1$, $3$, $9$, $25$, $65$:
 * $161 = 5 \times 2^5 + 1$


 * The $7$th inconsummate number after $62$, $63$, $65$, $75$, $84$, $95$:
 * $\nexists n \in \Z_{>0}: n = 161 \times \map {s_{10} } n$


 * The $32$nd positive integer $n$ such that no factorial of an integer can end with $n$ zeroes


 * The $60$th and largest (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $95$, $96$, $102$, $108$, $114$, $119$, $120$, $125$, $143$, $155$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$

Also see