Journal of Integer Sequences, Vol. 13 (2010), Article 10.3.1

Variations on Euclid's Formula for Perfect Numbers


Farideh Firoozbakht
Faculty of Mathematics & Computer Science
University of Isfahan
Khansar
Iran

Maximilian F. Hasler
Laboratoire CEREGMIA
Univ. Antilles-Guyane
Schoelcher
Martinique

Abstract:

We study several families of solutions to equations of the form σ(n) = An + B(n), where B is a function that may depend on properties of n.

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(Concerned with sequences A000043 A000203 A000217 A000396 A000668 A003307 A005820 A006516 A007539 A007691 A011251 A014224 A027687 A046060 A046061 A051783 A058959 A068390 A082730 A082731 A096502 A096818 A096821 A097215 A098855 A101260 A109080 A109321 A110082 A111592 A124621 A140863 A141545 A156555 A165701.)

Received July 31 2009; revised versions received February 18 2010. Published in Journal of Integer Sequences, February 23 2010.

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