A003416 Sociable numbers: smallest member of each cycle (conjectured).

12496, 14316, 1264460, 2115324, 2784580, 4938136, 7169104, 18048976, 18656380, 28158165, 46722700, 81128632, 174277820, 209524210, 330003580, 498215416, 805984760, 1095447416, 1236402232, 1276254780, 1799281330

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Numbers belonging to aliquot cycles of length greater than 2.

There is no proof that 564 (for example) is missing from this sequence (cf. A122726). - N. J. A. Sloane, Sep 17 2021

The lengths of the corresponding aliquot cycles are given by A052470. - Michel Marcus, Nov 15 2013

References

• R. K. Guy, Unsolved Problems Number Theory, B7.
• Paul Poulet, Parfaits, amiables et extensions, Editions Stevens, Bruxelles, 1918.
• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 91-92.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 174 Penguin Books 1987.

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..53
• Shyam Sunder Gupta, Perfect, Multiply Perfect, and Sociable Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 6, 185-207.
• Verner E. Hoggart, Jr., Letters to N. J. A. Sloane, 1974-1975
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 112
• David Moews, Perfect, amicable and sociable numbers
• David Moews, A list of currently known aliquot cycles of length greater than 2 [This list is not known to be complete.]
• Jan O. M. Pedersen, Tables of Aliquot Cycles [Broken link]
• Jan O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]
• Jan O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]
• Eric Weisstein's World of Mathematics, Sociable Numbers.

Crossrefs

Cf. A052470, A072890, A072891, A122726.

Extensions

Incorrect g.f. deleted by N. J. A. Sloane, Sep 20 2008

Added "conjectured" to definition. - N. J. A. Sloane, Sep 17 2021