 Base-p digit sum

ID: base-p-digit-sum

n = \sum_{r \geq 0} α_{r} p^{r}, 0 \leq α_{r} < p,

then the base-

p

d_{p} (n) = \sum_{r} α_{r}

. The Legendre formula can equivalently be written

v_{p} (n!) = \frac{n - d _{p} ( n )}{p - 1} .

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