## Pizza Toppings

### Problem 281

Published on Friday, 5th March 2010, 01:00 pm; Solved by 562; Difficulty rating: 55%You are given a pizza (perfect circle) that has been cut into `m`·`n` equal pieces and you want to have exactly one topping on each slice.

Let `f`(`m`,`n`) denote the number of ways you can have toppings on the pizza with `m` different toppings (`m` ≥ 2), using each topping on exactly `n` slices (`n` ≥ 1).

Reflections are considered distinct, rotations are not.

Thus, for instance, `f`(2,1) = 1, `f`(2,2) = `f`(3,1) = 2 and `f`(3,2) = 16. `f`(3,2) is shown below:

Find the sum of all `f`(`m`,`n`) such that `f`(`m`,`n`) ≤ 10^{15}.