The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A299701 Number of distinct subset-sums of the integer partition with Heinz number n. 39
 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 5, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 4, 6, 2, 7, 2, 6, 4, 4, 4, 7, 2, 4, 4, 7, 2, 8, 2, 6, 6, 4, 2, 7, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 8, 2, 4, 5, 7, 4, 8, 2, 6, 4, 7, 2, 8, 2, 4, 6, 6, 4, 8, 2, 8, 5, 4, 2, 9, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS An integer n is a subset-sum of an integer partition y if there exists a submultiset of y with sum n. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..20000 FORMULA a(n) <= A000005(n) and a(n) = A000005(n) iff n is the Heinz number of a knapsack partition (A299702). EXAMPLE The subset-sums of (5,1,1,1) are {0, 1, 2, 3, 5, 6, 7, 8} so a(88) = 8. The subset-sums of (4,3,1) are {0, 1, 3, 4, 5, 7, 8} so a(70) = 7. MATHEMATICA Table[Length[Union[Total/@Subsets[Join@@Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]], {n, 100}] CROSSREFS Cf. A000005, A000041, A000720, A001222, A056239, A108917, A112798, A122111, A122768, A215366, A276024, A284640, A296150, A299702. Sequence in context: A327527 A337454 A289849 * A286605 A035149 A074848 Adjacent sequences:  A299698 A299699 A299700 * A299702 A299703 A299704 KEYWORD nonn AUTHOR Gus Wiseman, Feb 17 2018 STATUS approved

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

Last modified May 20 09:27 EDT 2022. Contains 353871 sequences. (Running on oeis4.)