50

Number

$50$ (fifty) is:

$2 \times 5^2$

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 $2$nd term of the $1$st $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:

$\tuple {49, 50, 51, 52, 53}$

The $4$th hexagonal pyramidal number after $1$, $7$, $22$:

$50 = 1 + 6 + 15 + 28$

The $4$th noncototient after $10$, $26$, $34$:

$\nexists m \in \Z_{>0}: m - \map \phi m = 50$

where $\map \phi m$ denotes the Euler $\phi$ function

The $5$th nontotient after $14$, $26$, $34$, $38$:

$\nexists m \in \Z_{>0}: \map \phi m = 50$

where $\map \phi m$ denotes the Euler $\phi$ function

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.

The $34$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $37$, $38$, $42$, $43$, $44$, $48$, $49$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$