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A326018

Heinz numbers of knapsack partitions such that no addition of one part up to the maximum is knapsack.

1925, 12155, 20995, 23375, 37145

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OFFSET

1,1

COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

An integer partition is knapsack if every submultiset has a different sum.

The enumeration of these partitions by sum is given by A326016.

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

The sequence of terms together with their prime indices begins:

1925: {3,3,4,5}

12155: {3,5,6,7}

20995: {3,6,7,8}

23375: {3,3,3,5,7}

37145: {3,7,8,9}

MATHEMATICA

ksQ[y_]:=UnsameQ@@Total/@Union[Subsets[y]];

Select[Range[2, 200], With[{phm=If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, ksQ[phm]&&Select[Table[Sort[Append[phm, i]], {i, Max@@phm}], ksQ]=={}]&]

CROSSREFS

Cf. A002033, A108917, A275972, A299702, A299729, A304793.

Cf. A325780, A325782, A325857, A325862, A325878, A325880, A326015, A326016.

Sequence in context: A135648 A363821 A255867 * A202051 A283949 A133301

Adjacent sequences: A326015 A326016 A326017 * A326019 A326020 A326021

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 03 2019

STATUS

approved