63

Number
$63$ (sixty-three) is:


 * $3^2 \times 7$


 * The $3$rd of the $1$st ordered quadruple of consecutive integers that have sigma values which are strictly increasing:
 * $\map \sigma {61} = 62$, $\map \sigma {62} = 96$, $\map \sigma {63} = 104$, $\map \sigma {64} = 127$


 * The $2$nd inconsummate number after $62$:
 * $\nexists n \in \Z_{>0}: n = 63 \times \map {s_{10} } n$


 * The $4$th Woodall number after $1$, $7$, $23$:
 * $63 = 4 \times 2^4 - 1$


 * The $15$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $\ldots$


 * One of the cycle of $5$ numbers to which Kaprekar's process on $2$-digit numbers converges:
 * $63 \to 27 \to 45 \to 09 \to 81 \to 63$

Also see