2501

Number

$2501$ (two thousand, five hundred and one) is:

$41 \times 61$

The $4$th positive integer after $353$, $651$, $2487$ such that its fourth power is the sum of $4$ other fourth powers of positive integers with no common factors:

$2501^4 = 1130^4 + 1190^4 + 1432^4 + 2365^4$

The $41$st pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $1820$, $1926$, $2035$, $2147$, $2262$, $2380$:

$2501 = \ds \sum_{k \mathop = 1}^{41} \paren {3 k - 2} = \dfrac {41 \paren {3 \times 41 - 1} } 2$

The $81$st generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $2072$, $2147$, $2185$, $2262$, $2301$, $2380$, $2420$:

$2501 = \ds \sum_{k \mathop = 1}^{41} \paren {3 k - 2} = \dfrac {41 \paren {3 \times 41 - 1} } 2$