100

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


 * $2^2 \times 5^2$


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


 * The $2$nd power of $10$ after $(1)$, $10$:
 * $100 = 10^2$


 * The $4$th after $2$, $5$ and $10$ of $4$ numbers whose letters, when spelt in French, are in alphabetical order:
 * cent


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


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


 * The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $9$ different ways


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


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


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


 * 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 $23$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 $49$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.

Also see

 * 100 using Digits from 1 to 9