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A233553 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5. Groups of 5 subsequent terms list the five members in increasing size.

%I A233553 #47 Aug 08 2025 14:19:43
%S A233553 53542288800,59509850400,59999219280,60074174160,61695597600,
%T A233553 67154527440,68763895200,69626138400,71957405520,72598125600,
%U A233553 67509842400,72747675000,73605331800,75710489400,78953074200,87113426400,88410722400,89398663200,96058282320,96369633360
%N A233553 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5. Groups of 5 subsequent terms list the five members in increasing size.
%C A233553 The 5-tuple starting with 53542288800 was given by _Donovan Johnson_. The common value of sigma(x) is 294821130240.
%C A233553 A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by _Michel Marcus_ on Dec 09 2013. The common value of sigma(x) is 285857616844800.
%C A233553 A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by _Yasutoshi Kohmoto_ in 2008, cf. link to SeqFan post.
%C A233553 There are different definitions for amicable k-tuples, cf. link to MathWorld.
%H A233553 John Cerkan, <a href="/A233553/b233553.txt">Table of n, a(n) for n = 1..45</a>
%H A233553 John Cerkan, <a href="/A233553/a233553_1.txt">More terms, with gaps.</a>
%H A233553 Yasutoshi Kohmoto, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2008-November/000217.html">Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v</a>, SeqFan list, Nov 23 2008
%H A233553 Yasutoshi Kohmoto, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-December/012089.html">Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v</a>, SeqFan list, Dec 09 2013
%H A233553 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AmicableTriple.html">Amicable Triple</a>.
%Y A233553 Cf. A273928, A273930, A273931, A273933, A273934, A273936 (5-tuples).
%Y A233553 Cf. A036471 - A036474 and A116148 (quadruples).
%Y A233553 Cf. A125490 - A125492 and A137231 (triples).
%K A233553 nonn,hard
%O A233553 1,1
%A A233553 _M. F. Hasler_, Dec 12 2013
%E A233553 More terms from _John Cerkan_, Jun 05 2016