100

Number
$100$ (one hundred or a hundred) is:


 * $2^2 \times 5^2$


 * The $10$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$:
 * $100 = 10 \times 10$


 * The $8$th second pentagonal number after $2, 7, 15, 26, 40, 57, 77$:
 * $100 = \dfrac {8 \left({3 \times 8 + 1}\right)} 2$


 * The $16$th generalized pentagonal number after $1, 2, 5, 7, 12, 15, 22, 26, 35, 40, 51, 57, 70, 77, 92$:
 * $100 = \dfrac {8 \left({3 \times 8 + 1}\right)} 2$


 * The sum of the first $4$ cubes:
 * $100 = 1^3 + 2^3 + 3^3 + 4^3$


 * The $14$th powerful number after $1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81$


 * The $8$th noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$:
 * $\nexists m \in \Z_{>0}: m - \phi \left({m}\right) = 100$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The $23$rd semiperfect number after $6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96$:
 * $100 = 5 + 20 + 25 + 50$


 * The $20$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$, $44$, $49$, $68$, $70$, $79$, $82$, $86$, $91$, $94$, $97$:
 * $100 \to 1^2 + 0^2 + 0^2 = 1$


 * The $49$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $61$, $65$, $66$, $67$, $72$, $77$, $80$, $81$, $84$, $89$, $94$, $95$, $96$ which cannot be expressed as the sum of distinct pentagonal numbers.


 * The $4$th of $4$ numbers whose letters, when spelt in French, are in alphabetical order:
 * cent

Also see

 * 100 using Digits from 1 to 9