data/problems/429.yml
---
:id: 429
:name: Sum of squares of unitary divisors
:url: https://projecteuler.net/problem=429
:content: "A unitary divisor <var>d</var> of a number <var>n</var> is a divisor of
<var>n</var> that has the property gcd(<var>d, n/d</var>) = 1. \nThe unitary divisors
of 4! = 24 are 1, 3, 8 and 24. \nThe sum of their squares is 1<sup>2</sup> + 3<sup>2</sup>
+ 8<sup>2</sup> + 24<sup>2</sup> = 650.\n\nLet S(<var>n</var>) represent the sum
of the squares of the unitary divisors of <var>n</var>. Thus S(4!)=650.\n\nFind
S(100 000 000!) modulo 1 000 000 009.\n\n"