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.
LINKS
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
KEYWORD
nonn
AUTHOR
Jeppe Stig Nielsen, Jun 23 2015
STATUS
approved