cp's OEIS Frontend

A360678 Sum of the left half (inclusive) of the prime indices of n.

%I A360678 #6 Mar 07 2023 22:10:21
%S A360678 0,1,2,1,3,1,4,2,2,1,5,2,6,1,2,2,7,3,8,2,2,1,9,2,3,1,4,2,10,3,11,3,2,
%T A360678 1,3,2,12,1,2,2,13,3,14,2,4,1,15,3,4,4,2,2,16,3,3,2,2,1,17,2,18,1,4,3,
%U A360678 3,3,19,2,2,4,20,3,21,1,5,2,4,3,22,3,4,1
%N A360678 Sum of the left half (inclusive) of the prime indices of n.
%C A360678 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 A360678 A360676(n) + A360679(n) = A001222(n).
%F A360678 A360677(n) + A360678(n) = A001222(n).
%e A360678 The prime indices of 810 are {1,2,2,2,2,3}, with left half (inclusive) {1,2,2}, so a(810) = 5.
%e A360678 The prime indices of 3675 are {2,3,3,4,4}, with left half (inclusive) {2,3,3}, so a(3675) = 8.
%t A360678 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360678 Table[Total[Take[prix[n],Ceiling[Length[prix[n]]/2]]],{n,100}]
%Y A360678 Positions of first appearances are 1 and A001248.
%Y A360678 Positions of 1's are A001747.
%Y A360678 These partitions are counted by A360675 with rows reversed.
%Y A360678 The exclusive version is A360676.
%Y A360678 The right version is A360679.
%Y A360678 A112798 lists prime indices, length A001222, sum A056239, median* A360005.
%Y A360678 A360616 gives half of bigomega (exclusive), inclusive A360617.
%Y A360678 A360673 counts multisets by right sum (exclusive), inclusive A360671.
%Y A360678 First for prime indices, second for partitions, third for prime factors:
%Y A360678 - A360676 gives left sum (exclusive), counted by A360672, product A361200.
%Y A360678 - A360677 gives right sum (exclusive), counted by A360675, product A361201.
%Y A360678 - A360678 gives left sum (inclusive), counted by A360675, product A347043.
%Y A360678 - A360679 gives right sum (inclusive), counted by A360672, product A347044.
%Y A360678 Cf. A026424, A280076, A359912, A360006, A360457.
%K A360678 nonn
%O A360678 1,3
%A A360678 _Gus Wiseman_, Mar 05 2023