MathDB

Call a natural number

n{}

interesting if any natural number not exceeding

n{}

can be represented as the sum of several (possibly one) pairwise distinct positive divisors of

n{}

.
[*]Find the largest three-digit interesting number. [*]Prove that there are arbitrarily large interesting numbers other than the powers of two.
Proposed by N. Agakhanov

M2694

Problems(1)