2465

Number
$2465$ (two thousand, four hundred and sixty-five) is:


 * $5 \times 17 \times 29$


 * The $29$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $1281$, $1408$, $1541$, $1680$, $1825$, $1976$, $2133$, $2296$:
 * $2465 = \displaystyle \sum_{k \mathop = 1}^{29} \left({6 k - 5}\right) = 29 \left({3 \times 29 - 2}\right)$


 * The $9$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$, $2047$:
 * $2^{2465} \equiv 2 \pmod {2465}$: $2465 = 5 \times 17 \times 29$


 * The $11$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$, $1541$, $1729$, $1891$:
 * $3^{2465} \equiv 3 \pmod {2465}$


 * The $4$th Carmichael number after $561$, $1105$, $1729$:
 * $\forall a \in \Z: a \perp 2465: a^{2464} \equiv 1 \pmod {2465}$


 * The magic constant of the order $17$ magic square:
 * $2465 = \dfrac {17 \left({17^2 + 1}\right)} 2$


 * The magic constant of a magic square of order $17$, after $1$, $(5)$, $15$, $34$, $\ldots$, $870$, $1105$, $1379$, $1695$, $2056$:
 * $2465 = \displaystyle \dfrac 1 {17} \sum_{k \mathop = 1}^{17^2} k = \dfrac {17 \paren {17^2 + 1} } 2$