Munich Personal RePEc Archive

More properties about odd perfect numbers

Berdellima, Arian (2011): More properties about odd perfect numbers.

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Abstract

As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is called the special prime. In this work we show that p≥13 and if q∈{3,5} and q|n then either gcd⁡(q,σ(m^2 ))=1 or gcd⁡(q,σ(p^α ))=1.

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