A search for aliquot cycles below 10¹⁰

Moews, David; Moews, Paul C.

doi:10.1090/S0025-5718-1991-1094955-5

A search for aliquot cycles below $10^ {10}$
HTML articles powered by AMS MathViewer

by David Moews and Paul C. Moews PDF

Math. Comp. 57 (1991), 849-855 Request permission

Abstract:

A search for aliquot k-cycles below ${10^{10}}$ with $k \geq 3$ is described. Two new 4-cycles are exhibited. Six new 4-cycles not below ${10^{10}}$ are also exhibited.

References

Walter Borho, Über die Fixpunkte der $k$-fach iterierten Teilersummenfunktion, Mitt. Math. Gesellsch. Hamburg 9 (1969), no. 5, 34–48 (1969) (German). MR 0253976
Henri Cohen, On amicable and sociable numbers, Math. Comp. 24 (1970), 423–429. MR 271004, DOI 10.1090/S0025-5718-1970-0271004-6

Amicable pairs of Euler’s first form

10

J. S. Devitt, Richard K. Guy, and J. L. Selfridge, Third report on aliquot sequences, Proceedings of the Sixth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1976) Congress. Numer., XVIII, Utilitas Math., Winnipeg, Man., 1977, pp. 177–204. MR 532697
P. Erdös, On amicable numbers, Publ. Math. Debrecen 4 (1955), 108–111. MR 69198
P. Erdős, On asymptotic properties of aliquot sequences, Math. Comp. 30 (1976), no. 135, 641–645. MR 404115, DOI 10.1090/S0025-5718-1976-0404115-8
Achim Flammenkamp, New sociable numbers, Math. Comp. 56 (1991), no. 194, 871–873. MR 1052094, DOI 10.1090/S0025-5718-1991-1052094-3

25

H. J. J. te Riele, Computation of all the amicable pairs below $10^{10}$, Math. Comp. 47 (1986), no. 175, 361–368, S9–S40. With a supplement. MR 842142, DOI 10.1090/S0025-5718-1986-0842142-3

The density of the abundant numbers

20