cp's OEIS Frontend

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

%I A366128 #9 Mar 02 2024 01:26:02
%S A366128 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 A366128 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 A366128 1,2,1,0,1,2,1,3,1,4,1,0,1,2,1,0,1,2,1
%N A366128 Least non-subset-sum of the multiset of prime indices of n.
%C A366128 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 A366128 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 A366128 The prime indices of 3906 are {1,2,2,4,11}, with least non-subset-sum 10, so a(3906) = 10.
%t A366128 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A366128 nmz[y_]:=Complement[Range[Total[y]],Total/@Subsets[y]];
%t A366128 Table[If[nmz[prix[n]]=={},0,Min@@nmz[prix[n]]],{n,100}]
%Y A366128 Positions of ones are A005408.
%Y A366128 Positions of twos appear to be A091999.
%Y A366128 Zeros are A325781, nonzeros A325798.
%Y A366128 For greatest instead of least we have A365920 (Frobenius number).
%Y A366128 The triangle for this rank statistic is A365921 (partitions with least non-subset-sum k).
%Y A366128 A055932 lists numbers whose prime indices cover an initial interval.
%Y A366128 A056239 adds up prime indices, row sums of A112798.
%Y A366128 A073491 lists numbers with gap-free prime indices.
%Y A366128 A238709/A238710 count partitions by least/greatest difference.
%Y A366128 A342050/A342051 have prime indices with odd/even least gap.
%Y A366128 Cf. A001223, A079068, A257993, A286469, A286470, A339662, A339886.
%K A366128 nonn
%O A366128 1,10
%A A366128 _Gus Wiseman_, Oct 06 2023