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A299702 Heinz numbers of knapsack partitions. 61
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An integer partition is knapsack if every distinct submultiset has a different 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..68.

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, A299729.

Sequence in context: A085235 A160453 A325778 * A027855 A031996 A023753

Adjacent sequences:  A299699 A299700 A299701 * A299703 A299704 A299705

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 17 2018

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)