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A090615
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Smallest member of sociable quadruples.
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14
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1264460, 2115324, 2784580, 4938136, 7169104, 18048976, 18656380, 28158165, 46722700, 81128632, 174277820, 209524210, 330003580, 498215416, 1236402232, 1799281330, 2387776550, 2717495235, 2879697304, 3705771825, 4424606020, 4823923384, 5373457070, 8653956136
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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)
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REFERENCES
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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.
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LINKS
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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.
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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(22)-a(24) from Flammenkamp (1991) and Moews and Moews (1991) added by Amiram Eldar, Mar 24 2024
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STATUS
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approved
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