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

1,1

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.

P. Poulet, Parfaits, amiables et extensions, Editions Stevens, Bruxelles, 1918.

D. 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

V. E. Hoggart, Jr., Letters to N. J. A. Sloane, 1974-1975

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 112

D. Moews, Perfect, amicable and sociable numbers

D. Moews, A list of currently known aliquot cycles of length greater than 2 [This list is not known to be complete.]

J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]

J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]

J. 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.

Sequence in context: A232104 A122726 A072891 * A178278 A335989 A220026

Adjacent sequences: A003413 A003414 A003415 * A003417 A003418 A003419

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

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

Status

approved