This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A255215 #20 Jun 24 2015 19:07:27
%S A255215 1,220,284,1184,1210,1980,2016,2556,2620,2924,5020,5564,6232,6368,
%T A255215 9180,9504,10744,10856,11556,12285,14595,17296,18416,21168,22200,
%U A255215 23940,27312,31284,32136,37380,38940,39480,40068,40608,41412,41952,42168,43890,46368,47124
%N A255215 Numbers that belong to at least one amicable tuple.
%C A255215 Call a finite set {x_1, x_2, ..., x_k} of natural numbers (the x_i are pairwise distinct) an amicable k-tuple iff sigma(x_1)=sigma(x_2)=...=sigma(x_k)=x_1+x_2+...+x_k. Here sigma=A000203. For k=1, the only possible amicable one-tuple is {1}. For k=2 we get the classical amicable pairs (A063990). k=3 is amicable triples (A125490), k=4 amicable quadruples (A036471), and so on. A natural number n belongs to this sequence if and only if n is a member of some amicable k-tuple.
%C A255215 By definition, this sequence contains no duplicates.
%C A255215 For k<>2, an amicable k-tuple is not an aliquot cycle.
%H A255215 Jeppe Stig Nielsen, <a href="/A255215/b255215.txt">Table of n, a(n) for n = 1..361</a>
%e A255215 1 belongs to this sequence because {1} is considered an amicable one-tuple.
%e A255215 284 belongs to this sequence because {220, 284} is an amicable pair.
%e A255215 2016 belongs to this sequence because {1980, 2016, 2556} is an amicable triple.
%e A255215 38940 is included in this sequence only once even if both {38940, 40068, 41952} and {38940, 40608, 41412} are amicable.
%e A255215 1000 does not belong to this sequence. To prove that, note that sigma(1000)=2340. Then find all x such that sigma(x)=2340, these are 792, 1000, 1062, 1305, 1611, 1945, 2339. Run through all subsets of 792, 1000, 1062, 1305, 1611, 1945, 2339 that include 1000 to verify that no such subset has a sum of 2340.
%e A255215 A tuple (or multiset) like {1560, 1740, 1740} where some element(s) are repeated, is not allowed here, and neither 1560 nor 1740 belongs to this sequence.
%o A255215 (PARI) (notSubsetSum(desiredSum, searchSet) = { /* strongly inspired by is_A006037 function from A006037 */ local(t); /* return nonzero iff desiredSum is not the sum of a subset of searchSet */ setsearch( Set(searchSet), desiredSum ) & return /* equal to one element of searchSet */; while( #searchSet & searchSet[ #searchSet]>desiredSum, searchSet=vecextract(searchSet, "^-1")); desiredSum >= (t = sum(i=1, #searchSet, searchSet[i])) & return( desiredSum-t /* nonzero if desiredSum>t */ ); desiredSum > searchSet[ #searchSet] & ! notSubsetSum( desiredSum - searchSet[ #searchSet], searchSet=vecextract( searchSet, "^-1" )) & return; notSubsetSum( desiredSum, searchSet ) }); (othersWithSameSigma(n) = { s=sigma(n); [ x | x<-[1..s-1] , sigma(x)==s&&x!=n ] }); (is_A255215(x) = !notSubsetSum(sigma(x)-x, othersWithSameSigma(x)))
%Y A255215 Cf. A000203, A063990, A125490, A036471.
%Y A255215 Cf. A259307 (duplicates allowed in tuple).
%K A255215 nonn
%O A255215 1,2
%A A255215 _Jeppe Stig Nielsen_, Feb 17 2015