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Sum of squares of unitary divisors

Problem 429

Published on 26 May 2013 at 04:00 am [Server Time]

A unitary divisor d of a number n is a divisor of n that has the property gcd(d, n/d) = 1.
The unitary divisors of 4! = 24 are 1, 3, 8 and 24.
The sum of their squares is 12 + 32 + 82 + 242 = 650.

Let S(n) represent the sum of the squares of the unitary divisors of n. Thus S(4!)=650.

Find S(100 000 000!) modulo 1 000 000 009.


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