50

Number
$50$ (fifty) is:
 * $2 \times 5^2$


 * The $4$th hexagonal pyramidal number after $1, 7, 22$:
 * $50 = 1 + 6 + 15 + 28$


 * The $5$th nontotient after $14, 26, 34, 38$:
 * $\nexists m \in \Z_{>0}: \phi \left({m}\right) = 50$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The $4$th noncototient after $10, 26, 34$:
 * $\nexists m \in \Z_{>0}: m - \phi \left({m}\right) = 50$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The $2$nd term of the $1$st $5$-tuple of consecutive integers have the property that they are not values of the $\sigma$ function $\sigma \left({n}\right)$ for any $n$:
 * $\left({49, 50, 51, 52, 53}\right)$


 * The $1$st positive integer which can be expressed as the sum of two square numbers in two or more different ways:
 * $50 = 7^2 + 1^2 = 5^2 + 5^2$


 * The $31$st positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $33$, $37$, $38$, $42$, $43$, $44$, $45$, $46$, $49$ which cannot be expressed as the sum of distinct pentagonal numbers.

Also see