2023 IOQM/Problem 29
Problem
A positive integer is called
if
can be written in one and only
one way as
for some positive integers
, where
and
. (For example 6 is beautiful
since 6 = 3 · 2 · 1 = 3 + 2 + 1 , and this is unique. But 8 is not beautiful since
8 = 4 + 2 + 1 + 1 = 4 · 2 · 1 · 1 as well as 8 = 2 + 2 + 2 + 1 + 1 = 2 · 2 · 2 · 1 · 1 , so
uniqueness is lost.) Find the largest beautiful number less than 100.