95

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Number

$95$ (ninety-five) is:

$5 \times 19$

The $3$rd 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 $5$th Thabit number after $(2)$, $5$, $11$, $23$, $47$:

$95 = 3 \times 2^5 - 1$

The $5$th hexagonal pyramidal number after $1$, $7$, $22$, $50$:

$95 = 1 + 6 + 15 + 28 + 45 = \ds \sum_{k \mathop = 1}^5 k \paren {2 k - 1} = \dfrac {5 \paren {5 + 1} \paren {4 \times 5 - 1} } 6$

The $6$th inconsummate number after $62$, $63$, $65$, $75$, $84$:

$\nexists n \in \Z_{>0}: n = 95 \times \map {s_{10} } n$

The $33$rd semiprime:

$95 = 5 \times 19$

The $47$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $61$, $65$, $66$, $67$, $72$, $77$, $80$, $81$, $84$, $89$, $94$ which cannot be expressed as the sum of distinct pentagonal numbers.

The $50$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $77$, $78$, $79$, $84$, $90$, $91$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$