MathDB

Two positive integers

n,m\ge 2

are called allies if when written as a product of primes (not necessarily different):

n=p_1p_2...p_s

and

m=q_1q_2...q_t

, turns out that:

p_1 + p_2 + ... + p_s = q_1 + q_2 + ... + q_t

(a) Show that the biggest ally of any positive integer has to have only

2

and

3

in its prime factorization. (b) Find the biggest number which is allied of

2021

Problem Statement