%I #9 Mar 02 2024 01:26:02

%S 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,

%T 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,

%U 1,2,1,0,1,2,1,3,1,4,1,0,1,2,1,0,1,2,1

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

%C 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.

%C 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.

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

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t nmz[y_]:=Complement[Range[Total[y]],Total/@Subsets[y]];

%t Table[If[nmz[prix[n]]=={},0,Min@@nmz[prix[n]]],{n,100}]

%Y Positions of ones are A005408.

%Y Positions of twos appear to be A091999.

%Y Zeros are A325781, nonzeros A325798.

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

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

%Y A055932 lists numbers whose prime indices cover an initial interval.

%Y A056239 adds up prime indices, row sums of A112798.

%Y A073491 lists numbers with gap-free prime indices.

%Y A238709/A238710 count partitions by least/greatest difference.

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

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

%K nonn

%O 1,10

%A _Gus Wiseman_, Oct 06 2023