

A299729


Heinz numbers of nonknapsack partitions.


14



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
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OFFSET

1,1


COMMENTS

An integer partition is nonknapsack 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: A009096 A010814 A098714 * A325777 A108938 A085236
Adjacent sequences: A299726 A299727 A299728 * A299730 A299731 A299732


KEYWORD

nonn


AUTHOR

Gus Wiseman, Feb 17 2018


STATUS

approved



