Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-02T19:27:33.201Z Has data issue: false hasContentIssue false

The Factors of a Square-Free Integer

Published online by Cambridge University Press:  20 November 2018

R.D. James*
Affiliation:
University of British Columbia Vancouver
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note is concerned with the number C(n) of ordered non-trivial factorizations of an integer n in the special case where n is square free. If F (m) denotes C(p1…Pm) where pi. are distinct primes, it is shown that

and that

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Long, Calvin T., Addition theorems for sets of integers. Pacific J. Math. 23 (1967) 107-112.Google Scholar
2. MacMahon, P. A., The theory of perfect partitions and the composition of multipartite numbers. Mess. Math. 20 (1891) 103-119.Google Scholar
3. MacMahon, P.A., Memoir on the theory of compositions of numbers. Philos. Trans. Roy. Soc. London (A) 184 (1893) 835-901.Google Scholar
4. Niven, Ivan, Mathematics of choice. (Random House, New York, 1965).Google Scholar
5. Riordan, John, An introduction to combinatorial analysis. (Wiley, New York, 1958).Google Scholar