A299729 Heinz numbers of non-knapsack partitions.

12, 24, 30, 36, 40, 48, 60, 63, 70, 72, 80, 84, 90, 96, 108, 112, 120, 126, 132, 140, 144, 150, 154, 156, 160, 165, 168, 180, 189, 192, 198, 200, 204, 210, 216, 220, 224, 228, 240, 252, 264, 270, 273, 276, 280, 286, 288, 300, 308, 312, 315, 320, 324, 325

Offset

1,1

Comments

An integer partition is non-knapsack if there exist two different submultisets with the same sum. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Links

Table of n, a(n) for n=1..54.

Example

12 is the Heinz number of (2,1,1) which is not knapsack because 2 = 1 + 1.

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !UnsameQ@@Plus@@@Union[Rest@Subsets[primeMS[#]]]&]

Crossrefs

Cf. A056239, A108917, A112798, A275972, A276024, A284640, A296150, A299701, A299702.

Sequence in context: A334760 A098714 A334758 * A325777 A364532 A350056

Adjacent sequences: A299726 A299727 A299728 * A299730 A299731 A299732

Keyword

nonn

Author

Gus Wiseman, Feb 17 2018

Status

approved