## Finding numbers for which the sum of the squares of the digits is a square.

### Problem 171

Published on Saturday, 8th December 2007, 05:00 am; Solved by 1329

For a positive integer n, let f(n) be the sum of the squares of the digits (in base 10) of n, e.g.

f(3) = 32 = 9,
f(25) = 22 + 52 = 4 + 25 = 29,
f(442) = 42 + 42 + 22 = 16 + 16 + 4 = 36

Find the last nine digits of the sum of all n, 0 n 1020, such that f(n) is a perfect square.