

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
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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



