This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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