Problem 320

Factorials divisible by a huge integer

Let N(i) be the smallest integer n such that n! is divisible by (i!)^1234567890

Let S(u)=∑N(i) for 10 ≤ i ≤ u.

S(1000)=614538266565663.

Find S(1 000 000) mod 10¹⁸.

能被巨大整数整除的阶乘

记N(i)是使得n!被(i!)^1234567890整除的最小n值。

记S(u)=∑N(i)，其中10 ≤ i ≤ u。

已知S(1000)=614538266565663。

求S(1 000 000) mod 10¹⁸。