On an Integer's Infinitary Divisors

The notions of unitary divisor and biunitary divisor are extended in a natural fashion to give $k$-ary divisors, for any natural number $k$. We show that we may sensibly allow $k$ to increase indefinitely, and this leads to infinitary divisors. The infinitary divisors of an integer are described in...

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Bibliographic Details
Published in:Mathematics of computation 1990-01, Vol.54 (189), p.395-411
Main Author: Cohen, Graeme L.
Format: Article
Language:English
Subjects:
Fractals
Integers
Numbers
Citations: Items that this one cites
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Summary:The notions of unitary divisor and biunitary divisor are extended in a natural fashion to give $k$-ary divisors, for any natural number $k$. We show that we may sensibly allow $k$ to increase indefinitely, and this leads to infinitary divisors. The infinitary divisors of an integer are described in full, and applications to the obvious analogues of the classical perfect and amicable numbers and aliquot sequences are given.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1990-0993927-5