The Abundancy Index of Divisors of Odd Perfect Numbers

Details The Abundancy Index of Divisors of Odd Perfect Numbers The Abundancy Index of Divisors of Odd Perfect Numbers

2011-03-05

arxiv.org/abs/1103.1090v10

Mathematics

Number Theory

11 pages

Scientific paper

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

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