On an integer’s infinitary divisors

Cohen, Graeme L.

doi:10.1090/S0025-5718-1990-0993927-5

On an integer’s infinitary divisors
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Math. Comp. 54 (1990), 395-411 Request permission

Abstract:

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.

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