cp's OEIS Frontend

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

%I A003416 #70 Jul 14 2025 06:02:58
%S A003416 12496,14316,1264460,2115324,2784580,4938136,7169104,18048976,
%T A003416 18656380,28158165,46722700,81128632,174277820,209524210,330003580,
%U A003416 498215416,805984760,1095447416,1236402232,1276254780,1799281330
%N A003416 Sociable numbers: smallest member of each cycle (conjectured).
%C A003416 Numbers belonging to aliquot cycles of length greater than 2.
%C A003416 There is no proof that 564 (for example) is missing from this sequence (cf. A122726). - _N. J. A. Sloane_, Sep 17 2021
%C A003416 The lengths of the corresponding aliquot cycles are given by A052470. - _Michel Marcus_, Nov 15 2013
%D A003416 R. K. Guy, Unsolved Problems Number Theory, B7.
%D A003416 Paul Poulet, Parfaits, amiables et extensions, Editions Stevens, Bruxelles, 1918.
%D A003416 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 91-92.
%D A003416 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 174 Penguin Books 1987.
%H A003416 Jeppe Stig Nielsen, <a href="/A003416/b003416.txt">Table of n, a(n) for n = 1..53</a>
%H A003416 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_6">Perfect, Multiply Perfect, and Sociable Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 6, 185-207.
%H A003416 Verner E. Hoggart, Jr., <a href="/A003416/a003416.pdf">Letters to N. J. A. Sloane, 1974-1975</a>
%H A003416 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=112">Encyclopedia of Combinatorial Structures 112</a>
%H A003416 David Moews, <a href="http://djm.cc/amicable.html">Perfect, amicable and sociable numbers</a>
%H A003416 David Moews, <a href="http://djm.cc/sociable.txt">A list of currently known aliquot cycles of length greater than 2</a> [This list is not known to be complete.]
%H A003416 Jan O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]
%H A003416 Jan O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Via Internet Archive Wayback-Machine]
%H A003416 Jan O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]
%H A003416 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers.</a>
%Y A003416 Cf. A052470, A072890, A072891, A122726.
%K A003416 nonn
%O A003416 1,1
%A A003416 _N. J. A. Sloane_
%E A003416 Incorrect g.f. deleted by _N. J. A. Sloane_, Sep 20 2008
%E A003416 Added "conjectured" to definition. - _N. J. A. Sloane_, Sep 17 2021