0045

Forty-five is the smallest odd number that has more divisors than n + 1 {\displaystyle n+1}, and that has a larger sum of divisors than n + 1 {\displaystyle n+1}. It is the sixth positive integer with a square-prime prime factorization of the form p 2 q {\displaystyle p^{2}q}, with p {\displaystyle p} and q {\displaystyle q} prime. 45 has an aliquot sum of 33 that is part of an aliquot sequence composed of five composite numbers (45, 33, 15, 9, 4, 3, 1, and 0), all of which are rooted in the 3-aliquot tree. This is the longest aliquot sequence for an odd number up to 45.