cp's OEIS Frontend

A366528 Sum of odd prime indices of n.

%I A366528 #10 Oct 22 2023 16:42:30
%S A366528 0,1,0,2,3,1,0,3,0,4,5,2,0,1,3,4,7,1,0,5,0,6,9,3,6,1,0,2,0,4,11,5,5,8,
%T A366528 3,2,0,1,0,6,13,1,0,7,3,10,15,4,0,7,7,2,0,1,8,3,0,1,17,5,0,12,0,6,3,6,
%U A366528 19,9,9,4,0,3,21,1,6,2,5,1,0,7,0,14,23,2
%N A366528 Sum of odd prime indices of n.
%C A366528 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, sum A056239(n).
%F A366528 a(n) = A056239(n) - A366531(n).
%e A366528 The prime indices of 198 are {1,2,2,5}, so a(198) = 1+5 = 6.
%t A366528 Table[Total[Cases[FactorInteger[n], {p_?(OddQ@*PrimePi),k_}:>PrimePi[p]*k]],{n,100}]
%Y A366528 Zeros are A066207, counted by A035363.
%Y A366528 The triangle for this rank statistic is A113685, without zeros A365067.
%Y A366528 For count instead of sum we have A257991, even A257992.
%Y A366528 Nonzeros are A366322, counted by A086543.
%Y A366528 The even version is A366531, halved A366533, triangle A113686.
%Y A366528 A000009 counts partitions into odd parts, ranks A066208.
%Y A366528 A053253 = partitions with all odd parts and conjugate parts, ranks A352143.
%Y A366528 A066967 adds up sums of odd parts over all partitions.
%Y A366528 A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
%Y A366528 A162641 counts even prime exponents, odd A162642.
%Y A366528 A352142 = odd indices with odd exponents, counted by A117958.
%Y A366528 Cf. A000720, A055396, A130780, A171966, A174713, A325698, A325700, A366748.
%K A366528 nonn
%O A366528 1,4
%A A366528 _Gus Wiseman_, Oct 22 2023