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A299701 Number of distinct subset-sums of the integer partition with Heinz number n. 27
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: A301855 A080256 A289849 * A286605 A035149 A074848

Adjacent sequences:  A299698 A299699 A299700 * A299702 A299703 A299704

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 17 2018

STATUS

approved

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)