MathDB

A positive integer

n

is called

good

if it can be uniquely written simultaneously as a_1\plus{}a_2\plus{}...\plus{}a_k and as

a_1 a_2...a_k

, where

a_i

are positive integers and

k \ge 2

. (For example,

10

is good because 10\equal{}5\plus{}2\plus{}1\plus{}1\plus{}1\equal{}5 \cdot 2 \cdot 1 \cdot 1 \cdot 1 is a unique expression of this form). Find, in terms of prime numbers, all good natural numbers.

Problem Statement