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%I #11 Jul 09 2015 20:16:22
%S 1,6,28,120,220,284,496,672,1184,1210,1560,1740,1980,2016,2556,2620,
%T 2924,5020,5564,6232,6368,7380,7776,8128,9180,9504,10744,10856,11556,
%U 12285,14595,17296,18416,19260,20448,20640,20664,21168,21384,21924,22200,22428,22752
%N Numbers that belong to at least one amicable multiset.
%C 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.
%C By definition, A255215 is a subset because a set can be regarded as a special multiset.
%C 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.
%C The first amicable multiset that belongs to neither A255215 nor A007691 is {1740, 1740, 1560}.
%H Jeppe Stig Nielsen, <a href="/A259307/a259307.txt">List of all amicable multisets with a sigma value below 10^7</a>.
%o (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,[]))
%Y Cf. A255215, A007691, A259302, A259303, A259304, A259305, A259306.
%K nonn
%O 1,2
%A _Jeppe Stig Nielsen_, Jun 23 2015
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