MathDB
IOQM 2023-24 P-19

Source:

September 3, 2023

Problem Statement

For n∈Nn \in \mathbb{N}, let P(n)P(n) denote the product of the digits in nn and S(n)S(n) denote the sum of the digits in nn. Consider the set A={n∈N:P(n)A=\{n \in \mathbb{N}: P(n) is non-zero, square free and S(n)S(n) is a proper divisor of P(n)}P(n)\}. Find the maximum possible number of digits of the numbers in AA.
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