A090615 Smallest member of sociable quadruples.

1264460, 2115324, 2784580, 4938136, 7169104, 18048976, 18656380, 28158165, 46722700, 81128632, 174277820, 209524210, 330003580, 498215416, 1236402232, 1799281330, 2387776550, 2717495235, 2879697304, 3705771825, 4424606020, 4823923384, 5373457070, 8653956136

Offset: 1

Author

Eric W. Weisstein, Dec 06 2003

Keywords

• nonn

Comments

120 sociable numbers of order 4 are known as of Feb. 2003.

142 were known in 2007 (http://amicable.homepage.dk/knwnc4.htm).

201 are known in 2012.

210 were known in April 2013. - Michel Marcus, Nov 10 2013

From Amiram Eldar, Mar 24 2024: (Start)

The terms were found by:

a(1)-a(2) - Kenneth Dudley Fryer in 1965 (Honsberger, 1970; see also A072892)

a(3)-a(7), a(9) - Cohen (1970)

a(8) - Borho (1969)

a(10)-a(13) - independently by Richard David (1972; Devitt et al., 1976, Guy 1977) and Steve C. Root (Beeler et al. 1972)

a(14) - Steve C. Root in 1972

a(15)-a(22) - Flammenkamp (1991)

a(23)-a(24) - Moews and Moews (1991)

a(25)-a(27) - Moews and Moews (1993)

(End)

References

• Walter Borho, Über die Fixpunkte der k-fach iterierten Teilersummenfunktion, Mitt. Math. Gesellsch. Hamburg, Vol. 9, No. 5 (1969), pp. 34-48.
• Richard David, Letter to D. H. Lehmer, February 25 , 1972.
• 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.
• 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.
• Ross Honsberger, Ingenuity in Mathematics, Mathematical Association of America, 1970.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..48
• Michael Beeler, R. William Gosper and Richard C. Schroeppel, HAKMEM, MIT Artificial Intelligence Laboratory report AIM-239, Feb. 29, 1972, Item 61; HTML transcription.
• Karsten Blankenagel, Walter Borho, and Axel vom Stein, New amicable four-cycles, Math. Comp., Vol. 72, No. 244 (2003), pp. 2071-2076.
• Karsten Blankenagel and Walter Borho, New amicable four-cycles II, International Journal of Mathematics and Scientific Computing, Vol. 5, No. 1 (2015), pp. 49-51.
• Henri Cohen, On amicable and sociable numbers, Math. Comp., Vol. 24, No. 110 (1970), pp. 423-429.
• Achim Flammenkamp, New sociable numbers, Mathematics of Computation, Vol. 56, No. 194 (1991), pp. 871-873.
• Richard K. Guy and John L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.
• David Moews, A list of currently known aliquot cycles of length greater than 2.
• David Moews and Paul C. Moews, Aliquot cycles below 10^10, Mathematics of Computation, Volume 57, No. 196 (1991), pp. 849-855.
• David Moews and Paul C. Moews, A search for aliquot cycles and amicable pairs, Mathematics of computation, Vol. 61, No. 204 (1993), pp. 935-938.
• Jan Munch Pedersen, Known Sociable Numbers of order four, Tables of Aliquot Cycles.
• Eric Weisstein's World of Mathematics, Sociable Numbers.
• Wikipedia, Sociable number.

Crossrefs

Cf. A003023, A003416, A052470, A072892.

Extensions

a(22)-a(24) from Flammenkamp (1991) and Moews and Moews (1991) added by Amiram Eldar, Mar 24 2024