A259307 Numbers that belong to at least one amicable multiset.

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

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

Table of n, a(n) for n=1..43.

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