The abundancy index of divisors of odd perfect numbers

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Journal of Integer Sequences

Volume

15

Issue

4

Publication Date

9-3-2012

Abstract

If N = qkn2 is an odd perfect number, where q is the Euler prime, then we show that n < q is sufficient for Sorli's conjecture that k = νq(N) = 1 to hold. We also prove and that qk < 2/3n2, and that I(qk) < I(n), where I(x) is the abundancy index of x.

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Disciplines

Mathematics

Keywords

Perfect numbers; Numbers, Prime

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