OFFSET
1,10
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.
EXAMPLE
The prime indices of 3906 are {1,2,2,4,11}, with least non-subset-sum 10, so a(3906) = 10.
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}]
CROSSREFS
Positions of ones are A005408.
Positions of twos appear to be A091999.
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.
A073491 lists numbers with gap-free prime indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 06 2023
STATUS
approved