102

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Number

$102$ (one hundred and two) is:

$2 \times 3 \times 17$

The $3$rd positive integer after $1$, $7$ the sum of whose divisors is a cube:

$\map {\sigma_1} {102} = 216 = 6^3$

It is also the $2$nd of those positive integer after $1$ whose divisor count is also a cube:

$\map {\sigma_0} {102} = 8 = 2^3$

The $6$th sphenic number after $30$, $42$, $66$, $70$, $78$:

$102 = 2 \times 3 \times 17$

The smallest positive integer whose $7$th power can be expressed as the sum of $8$ other $7$th powers:

$102^7 = 12^7 + 35^7 + 53^7 + 58^7 + 64^7 + 83^7 + 85^7 + 90^7$

The $51$st positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $61$, $65$, $66$, $67$, $72$, $77$, $80$, $81$, $84$, $89$, $94$, $95$, $96$, $100$, $101$ which cannot be expressed as the sum of distinct pentagonal numbers.

The $52$nd (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $77$, $78$, $79$, $84$, $90$, $91$, $95$, $96$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$