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A293627 Number of knapsack factorizations whose factors sum to n. 3
1, 1, 1, 2, 2, 4, 4, 6, 8, 11, 12, 19, 21, 27, 34, 45, 51, 69, 77, 100, 117, 146 (list; graph; refs; listen; history; text; internal format)
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: A162417 A240012 A295261 * A264393 A094858 A029940

Adjacent sequences:  A293624 A293625 A293626 * A293628 A293629 A293630

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 23 2017

STATUS

approved

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Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)