MathDB

Define a function

f

on the positive integers as follows:

f(n) = m

, where

m

is the least positive integer such that

n

is a factor of

m^2

. Find the smallest integer

M

such that

\sqrt{M}

is both a product of prime numbers, of which there are at least

3

, and a factor of

\sum_{ d|M} f(d),

the sum of

f(d)

for all positive integers

d

that divide

M

Problem Statement