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

Author

Gus Wiseman, Oct 23 2017

Keywords

• nonn
• more

Comments

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

Examples

			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).
		

Crossrefs

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

Programs

Mathematica

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