A366128 Least non-subset-sum of the multiset of prime indices of n.

0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 3, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 4, 1, 3, 1, 2, 1, 0, 1, 2, 1, 3, 1, 4, 1, 0, 1, 2, 1, 0, 1, 2, 1

Offset: 1

Author

Gus Wiseman, Oct 06 2023

Keywords

• nonn

Comments

Least positive integer up to the sum of prime indices of n that is not the sum of prime indices of any divisor of n, or 0 if none exists.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The prime indices of 3906 are {1,2,2,4,11}, with least non-subset-sum 10, so a(3906) = 10.
		

Crossrefs

Positions of ones are A005408.

Positions of twos appear to be A091999.

Zeros are A325781, nonzeros A325798.

For greatest instead of least we have A365920 (Frobenius number).

The triangle for this rank statistic is A365921 (partitions with least non-subset-sum k).

A055932 lists numbers whose prime indices cover an initial interval.

A056239 adds up prime indices, row sums of A112798.

A073491 lists numbers with gap-free prime indices.

A238709/A238710 count partitions by least/greatest difference.

A342050/A342051 have prime indices with odd/even least gap.

Cf. A001223, A079068, A257993, A286469, A286470, A339662, A339886.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
nmz[y_]:=Complement[Range[Total[y]],Total/@Subsets[y]];
Table[If[nmz[prix[n]]=={},0,Min@@nmz[prix[n]]],{n,100}]