A294150 Number of knapsack partitions of n that are also knapsack factorizations.

1, 1, 1, 2, 2, 4, 4, 6, 8, 10, 12, 13, 20, 20, 29, 30, 41, 41, 56, 53, 81, 75

Offset: 1

Author

Gus Wiseman, Oct 23 2017

Keywords

• nonn
• more

Comments

a(n) is the number of finite multisets of positive integers summing to n such that every distinct submultiset has a different sum, and also every distinct submultiset has a different product.

Examples

			The a(12) = 13 partitions are:
(12),
(10 2), (9 3), (8 4), (7 5), (6 6),
(8 2 2), (7 3 2), (5 5 2), (5 4 3), (4 4 4),
(3 3 3 3),
(2 2 2 2 2 2).
		

Links

• R. Ehrenborg and M. Readdy, The Mobius function of partitions with restricted block sizes, Advances in Applied Mathematics, Volume 39, Issue 3, September 2007, Pages 283-292.

Crossrefs

Cf. A000041, A001055, A108917, A275972, A292886, A293627.

Programs

Mathematica

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