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Let f (N ) be the number of unordered factorizations of N , where a factorization is a way of writing N as a product of integers all larger than 1. For example, the factorizations of 30 are 2 · 3 · 5, 5 · 6, 3 · 10, 2 · 15, 30, so that f (30) = 5. The function f (N ), as a multiplicative analogue of the (additive) partition function p(N ), was first proposed by MacMahon, and its study was pursued by Oppenheim, Szekeres and Turán, and others. Recently, Zaharescu and Zaki showed that f (N ) isdoi:10.1090/s0002-9939-2012-11254-7 fatcat:2k6gkr3zinfyfhuuvximwy56oe