International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 213-216

Recursive formulae for the multiplicative partition function

Jun Kyo Kim and Sang Guen Hahn

Korea Advanced Institute of Science and Technology 373-1, Kusong Don, Yusung Gu, Taejon 305-701, Korea

Received 28 February 1996

Copyright © 1999 Jun Kyo Kim and Sang Guen Hahn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a positive integer n, let f(n) be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. This paper gives a recursive formula for the multiplicative partition function f(n).