The abundancy index of divisors of odd perfect numbers – Part II
نویسندگان
چکیده
In this note, we show that if N = q^kn^2 is an odd perfect number with special prime q, and not divisible by 3, then the inequality q < n holds. We give another unconditional proof for which independent of results Brown Starni.
منابع مشابه
The Abundancy Index of Divisors of Odd Perfect Numbers
If N = qkn2 is an odd perfect number, where q is the Euler prime, then we show that σ(n) ≤ qk is necessary and sufficient for Sorli’s conjecture that k = νq(N) = 1 to hold. It follows that, if k = 1 then the Euler prime q is the largest prime factor of N and that q > 10500. We also prove that qk < 23n 2.
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ژورنال
عنوان ژورنال: Notes on Number Theory and Discrete Mathematics
سال: 2021
ISSN: ['1310-5132', '2367-8275']
DOI: https://doi.org/10.7546/nntdm.2021.27.2.12-19