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 A259307 Numbers that belong to at least one amicable multiset. 8
 1, 6, 28, 120, 220, 284, 496, 672, 1184, 1210, 1560, 1740, 1980, 2016, 2556, 2620, 2924, 5020, 5564, 6232, 6368, 7380, 7776, 8128, 9180, 9504, 10744, 10856, 11556, 12285, 14595, 17296, 18416, 19260, 20448, 20640, 20664, 21168, 21384, 21924, 22200, 22428, 22752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Call a finite multiset {x_1, x_2, ..., x_k} of natural numbers (the x_i need not be distinct) an amicable multiset iff sigma(x_1)=sigma(x_2)=...=sigma(x_k)=x_1+x_2+...+x_k. By definition, A255215 is a subset because a set can be regarded as a special multiset. Also A007691 is a subset, since a k-perfect number corresponds to an amicable multiset in an obvious way. For example, since 120 is 3-perfect, the multiset {120, 120, 120} is amicable. The first amicable multiset that belongs to neither A255215 nor A007691 is {1740, 1740, 1560}. LINKS Jeppe Stig Nielsen, List of all amicable multisets with a sigma value below 10^7. PROG (PARI) /* write amicable multisets */ sMax=10^7; sigmaVals=vector(sMax, x, []); for(n=1, sMax, s=sigma(n); s<=sMax&sigmaVals[s]=concat(sigmaVals[s], [n])); (MultisetSum(numbers, desiredSum, track)=if(desiredSum<0, return); if(desiredSum==0, print(apply(x->numbers[x], track)); return); for(i=if(track, track[#track], 1), #numbers, MultisetSum(numbers, desiredSum-numbers[i], concat(track, [i])))); for(s=1, sMax, MultisetSum(sigmaVals[s], s, [])) CROSSREFS Cf. A255215, A007691, A259302, A259303, A259304, A259305, A259306. Sequence in context: A026014 A332208 A226853 * A183019 A183016 A282775 Adjacent sequences: A259304 A259305 A259306 * A259308 A259309 A259310 KEYWORD nonn AUTHOR Jeppe Stig Nielsen, Jun 23 2015 STATUS approved

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Last modified March 20 05:30 EDT 2023. Contains 361358 sequences. (Running on oeis4.)