cp's OEIS Frontend

A090615 Smallest member of sociable quadruples.

%I A090615 #34 Feb 16 2025 08:32:52
%S A090615 1264460,2115324,2784580,4938136,7169104,18048976,18656380,28158165,
%T A090615 46722700,81128632,174277820,209524210,330003580,498215416,1236402232,
%U A090615 1799281330,2387776550,2717495235,2879697304,3705771825,4424606020,4823923384,5373457070,8653956136
%N A090615 Smallest member of sociable quadruples.
%C A090615 120 sociable numbers of order 4 are known as of Feb. 2003.
%C A090615 142 were known in 2007 (http://amicable.homepage.dk/knwnc4.htm).
%C A090615 201 are known in 2012.
%C A090615 210 were known in April 2013. - _Michel Marcus_, Nov 10 2013
%C A090615 From _Amiram Eldar_, Mar 24 2024: (Start)
%C A090615 The terms were found by:
%C A090615   a(1)-a(2) - Kenneth Dudley Fryer in 1965 (Honsberger, 1970; see also A072892)
%C A090615   a(3)-a(7), a(9) - Cohen (1970)
%C A090615   a(8) - Borho (1969)
%C A090615   a(10)-a(13) - independently by Richard David (1972; Devitt et al., 1976, Guy 1977) and Steve C. Root (Beeler et al. 1972)
%C A090615   a(14) - Steve C. Root in 1972
%C A090615   a(15)-a(22) - Flammenkamp (1991)
%C A090615   a(23)-a(24) - Moews and Moews (1991)
%C A090615   a(25)-a(27) - Moews and Moews (1993)
%C A090615 (End)
%D A090615 Walter Borho, Über die Fixpunkte der k-fach iterierten Teilersummenfunktion, Mitt. Math. Gesellsch. Hamburg, Vol. 9, No. 5 (1969), pp. 34-48.
%D A090615 Richard David, Letter to D. H. Lehmer, February 25 , 1972.
%D A090615 John Stanley Devitt, Richard K. Guy, and John L. Selfridge, Third report on aliquot sequences, Proceedings of the Sixth Manitoba Conference on Numerical Mathematics, September 29 - October 2, 1976, Congressus Numerantium XVIII, University of Manitoba, Winnipeg, Manitoba, Utilitas Mathematics Publications, 1976, pp. 177-204.
%D A090615 Richard K. Guy, "Aliquot Sequences", in: Hans Zassenhaus (ed.), Number Theory and Algebra: Collected Papers Dedicated to Henry B. Mann, Arnold E. Ross, and Olga Taussky-Toddm, Academic Press Inc., 1977.
%D A090615 Ross Honsberger, Ingenuity in Mathematics, Mathematical Association of America, 1970.
%H A090615 Amiram Eldar, <a href="/A090615/b090615.txt">Table of n, a(n) for n = 1..48</a>
%H A090615 Michael Beeler, R. William Gosper and Richard C. Schroeppel, <a href="https://dspace.mit.edu/handle/1721.1/6086">HAKMEM</a>, MIT Artificial Intelligence Laboratory report AIM-239, Feb. 29, 1972, Item 61; <a href="https://www.inwap.com/pdp10/hbaker/hakmem/number.html">HTML transcription</a>.
%H A090615 Karsten Blankenagel, Walter Borho, and Axel vom Stein, <a href="https://doi.org/10.1090/S0025-5718-03-01489-3">New amicable four-cycles</a>, Math. Comp., Vol. 72, No. 244 (2003), pp. 2071-2076.
%H A090615 Karsten Blankenagel and Walter Borho, <a href="https://demovtu.veltech.edu.in/wp-content/uploads/2016/04/Paper-11-2015.pdf">New amicable four-cycles II</a>, International Journal of Mathematics and Scientific Computing, Vol. 5, No. 1 (2015), pp. 49-51.
%H A090615 Henri Cohen, <a href="https://doi.org/10.1090/S0025-5718-1970-0271004-6">On amicable and sociable numbers</a>, Math. Comp., Vol. 24, No. 110 (1970), pp. 423-429.
%H A090615 Achim Flammenkamp, <a href="https://doi.org/10.1090/S0025-5718-1991-1052094-3">New sociable numbers</a>, Mathematics of Computation, Vol. 56, No. 194 (1991), pp. 871-873.
%H A090615 Richard K. Guy and John L. Selfridge, <a href="/A003023/a003023.pdf">Interim report on aliquot series</a>, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.
%H A090615 David Moews, <a href="http://djm.cc/sociable.txt">A list of currently known aliquot cycles of length greater than 2</a>.
%H A090615 David Moews and Paul C. Moews, <a href="https://doi.org/10.1090/S0025-5718-1991-1094955-5">Aliquot cycles below 10^10</a>, Mathematics of Computation, Volume 57, No. 196 (1991), pp. 849-855.
%H A090615 David Moews and Paul C. Moews, <a href="https://doi.org/10.1090/S0025-5718-1993-1185249-X">A search for aliquot cycles and amicable pairs</a>, Mathematics of computation, Vol. 61, No. 204 (1993), pp. 935-938.
%H A090615 Jan Munch Pedersen, <a href="http://62.198.248.44/aliquot/knwnc4.htm">Known Sociable Numbers of order four</a>, Tables of Aliquot Cycles.
%H A090615 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers</a>.
%H A090615 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sociable_number">Sociable number</a>.
%Y A090615 Cf. A003023, A003416, A052470, A072892.
%K A090615 nonn
%O A090615 1,1
%A A090615 _Eric W. Weisstein_, Dec 06 2003
%E A090615 a(22)-a(24) from Flammenkamp (1991) and Moews and Moews (1991) added by _Amiram Eldar_, Mar 24 2024