A293627 Number of knapsack factorizations whose factors sum to n.

1, 1, 1, 2, 2, 4, 4, 6, 8, 11, 12, 19, 21, 27, 34, 45, 51, 69, 77, 100, 117, 146

Offset

1,4

Comments

A knapsack factorization is a finite multiset of positive integers greater than one such that every distinct submultiset has a different product.

Links

Table of n, a(n) for n=1..22.

Example

The a(12) = 19 partitions are:
(12),
(10 2), (9 3), (8 4), (7 5), (6 6),
(8 2 2), (7 3 2), (6 4 2), (6 3 3), (5 5 2), (5 4 3), (4 4 4),
(6 2 2 2), (5 3 2 2), (4 3 3 2), (3 3 3 3),
(3 3 2 2 2),
(2 2 2 2 2 2).

Mathematica

nn=22;
apsQ[y_]:=UnsameQ@@Times@@@Union[Rest@Subsets[y]];
Table[Length@Select[IntegerPartitions[n], apsQ], {n, nn}]

Crossrefs

Cf. A000041, A001055, A002033, A002865, A108917, A126796, A275972, A281116, A292886, A294150.

Sequence in context: A240012 A375134 A295261 * A264393 A362307 A094858

Adjacent sequences: A293624 A293625 A293626 * A293628 A293629 A293630

Keyword

nonn,more

Author

Gus Wiseman, Oct 23 2017

Status

approved