More properties about odd perfect numbers

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

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: perfect numbers; odd perfect numbers; special prime; greatest common divisor
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General; Z - Other Special Topics > Z0 - General

References

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2. G. G. Dandapat, J. L. Hunsucker, Carl Pomerance, Some New Results on Odd Perfect Numbers, Pacific Journal of Mathematics, Vol.57, No.2, 1975.

3. Wolfram MathWorld, Perfect Numbers, http://mathworld.wolfram.com/PerfectNumber.html, 2011.