Journal of the Ramanujan Mathematical Society
Volume 32, Issue 4, December 2017 pp. 417–430.
On the number of factorizations of an integer
Authors:
R. Balasubramanian and Priyamvad Srivastav
Author institution:Institute of Mathematical Sciences, Taramani, Chennai, India~600~113
Summary:
Let f(n) denote the number of unordered factorizations of a
positive integer n into factors larger than 1. We show that
the number of distinct values of f(n), less than or equal to
x, is at most exp (C √ log x/log log x
(1 + o(1))), where C = 2 π √ 2/3 and x
is sufficiently large. This improves upon a previous result of the
first author and F. Luca.
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