260

Number
$260$ (two hundred and sixty) is:


 * $2^2 \times 5 \times 13$


 * The $13$th second pentagonal number after $2, 7, 15, 26, 40, 57, 77, 100, 126, 155, 187, 222$:
 * $260 = \dfrac {13 \left({3 \times 13 + 1}\right)} 2$


 * The $26$th generalized pentagonal number after $1, 2, 5, 7, 12, 15, \ldots, 126, 145, 176, 187, 210, 222, 247$:
 * $260 = \dfrac {13 \left({3 \times 13 + 1}\right)} 2$


 * The $24$th noncototient after $10, 26, 34, 50, \ldots, 206, 218, 222, 232, 244$:
 * $\nexists m \in \Z_{>0}: m - \phi \left({m}\right) = 260$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The $13$th positive integer after $50, 65, 85, 125, 130, 145, 170, 185, 200, 205, 221, 250$ which can be expressed as the sum of two square numbers in two or more different ways:
 * $260 = 16^2 + 4^2 = 14^2 + 8^2$


 * The $51$st positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.