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%I #6 Mar 07 2023 22:10:16
%S 0,1,2,1,3,2,4,2,2,3,5,3,6,4,3,2,7,4,8,4,4,5,9,3,3,6,4,5,10,5,11,3,5,
%T 7,4,4,12,8,6,4,13,6,14,6,5,9,15,4,4,6,7,7,16,4,5,5,8,10,17,5,18,11,6,
%U 3,6,7,19,8,9,7,20,5,21,12,6,9,5,8,22,5,4
%N Sum of the right half (inclusive) of the 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 A360676(n) + A360679(n) = A001222(n).
%F A360677(n) + A360678(n) = A001222(n).
%e The prime indices of 810 are {1,2,2,2,2,3}, with right half (inclusive) {2,2,3}, so a(810) = 7.
%e The prime indices of 3675 are {2,3,3,4,4}, with right half (inclusive) {3,4,4}, so a(3675) = 11.
%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Total[Take[prix[n],-Ceiling[Length[prix[n]]/2]]],{n,100}]
%Y Positions of first appearances are 1 and A001248.
%Y The value k appears A360671(k) times, exclusive A360673.
%Y These partitions are counted by A360672 with rows reversed.
%Y The exclusive version is A360677.
%Y The left version is A360678.
%Y A112798 lists prime indices, length A001222, sum A056239, median* A360005.
%Y A360616 gives half of bigomega (exclusive), inclusive A360617.
%Y First for prime indices, second for partitions, third for prime factors:
%Y - A360676 gives left sum (exclusive), counted by A360672, product A361200.
%Y - A360677 gives right sum (exclusive), counted by A360675, product A361201.
%Y - A360678 gives left sum (inclusive), counted by A360675, product A347043.
%Y - A360679 gives right sum (inclusive), counted by A360672, product A347044.
%Y Cf. A026424, A359912, A360006, A360007, A360457.
%K nonn
%O 1,3
%A _Gus Wiseman_, Mar 05 2023
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