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%I #7 Oct 22 2023 16:42:40
%S 0,0,2,0,0,2,4,0,4,0,0,2,6,4,2,0,0,4,8,0,6,0,0,2,0,6,6,4,10,2,0,0,2,0,
%T 4,4,12,8,8,0,0,6,14,0,4,0,0,2,8,0,2,6,16,6,0,4,10,10,0,2,18,0,8,0,6,
%U 2,0,0,2,4,20,4,0,12,2,8,4,8,22,0,8,0,0,6
%N Sum of even prime indices of n.
%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.
%F a(n) = A056239(n) - A366528(n).
%e The prime indices of 198 are {1,2,2,5}, so a(198) = 2+2 = 4.
%t Table[Total[Cases[FactorInteger[n], {p_?(EvenQ@*PrimePi),k_}:>PrimePi[p]*k]],{n,100}]
%Y Zeros are A066208, counted by A000009.
%Y The triangle for the odd version is A113685, without zeros A365067.
%Y The triangle for this statistic is A113686, without zeros A174713.
%Y The odd version is A366528.
%Y The halved version is A366533.
%Y A066207 lists numbers with all even prime indices, counted by A035363.
%Y A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
%Y A239261 counts partitions with sum of odd parts = sum of even parts.
%Y A257991 counts odd prime indices, even A257992.
%Y A346697 adds up odd-indexed prime indices, even-indexed A346698.
%Y A366322 lists numbers with not all prime indices even, counted by A086543.
%Y Cf. A000720, A055396, A055922, A061395, A162641, A171966, A258117, A325698, A325700, A352140, A352141.
%K nonn
%O 1,3
%A _Gus Wiseman_, Oct 22 2023