MathDB

Let

n>4

be a positive integer, which is divisible by

4

. We denote by

A_n

the sum of the odd positive divisors of

n

. We also denote

B_n

the sum of the even positive divisors of

n

, excluding the number

n

itself. Find the least possible value of the expression

f(n)=B_n-2A_n,

for all possible values of

n

, as well as for which positive integers

n

this minimum value is attained.

Problem Statement