cp's OEIS Frontend

A360677 Sum of the right half (exclusive) of the prime indices of n.

%I A360677 #8 Mar 07 2023 22:10:32
%S A360677 0,0,0,1,0,2,0,1,2,3,0,2,0,4,3,2,0,2,0,3,4,5,0,3,3,6,2,4,0,3,0,2,5,7,
%T A360677 4,4,0,8,6,4,0,4,0,5,3,9,0,3,4,3,7,6,0,4,5,5,8,10,0,5,0,11,4,3,6,5,0,
%U A360677 7,9,4,0,4,0,12,3,8,5,6,0,4,4,13,0,6,7
%N A360677 Sum of the right half (exclusive) of the prime indices of n.
%C A360677 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 A360677 Last position of k is 2^(2k+1).
%F A360677 A360676(n) + A360679(n) = A001222(n).
%F A360677 A360677(n) + A360678(n) = A001222(n).
%e A360677 The prime indices of 810 are {1,2,2,2,2,3}, with right half (exclusive) {2,2,3}, so a(810) = 7.
%e A360677 The prime indices of 3675 are {2,3,3,4,4}, with right half (exclusive) {4,4}, so a(3675) = 8.
%t A360677 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360677 Table[Total[Take[prix[n],-Floor[Length[prix[n]]/2]]],{n,100}]
%Y A360677 Positions of 0's are 1 and A000040.
%Y A360677 Positions of last appearances are A004171.
%Y A360677 Positions of first appearances are A100484.
%Y A360677 These partitions are counted by A360672.
%Y A360677 The value k > 0 appears A360673(k) times, inclusive A360671.
%Y A360677 The left version is A360676.
%Y A360677 The inclusive version is A360679.
%Y A360677 A112798 lists prime indices, length A001222, sum A056239, median* A360005.
%Y A360677 A360616 gives half of bigomega (exclusive), inclusive A360617.
%Y A360677 First for prime indices, second for partitions, third for prime factors:
%Y A360677 - A360676 gives left sum (exclusive), counted by A360672, product A361200.
%Y A360677 - A360677 gives right sum (exclusive), counted by A360675, product A361201.
%Y A360677 - A360678 gives left sum (inclusive), counted by A360675, product A347043.
%Y A360677 - A360679 gives right sum (inclusive), counted by A360672, product A347044.
%Y A360677 Cf. A001248, A026424, A359908, A359912, A360006, A360457.
%K A360677 nonn
%O A360677 1,6
%A A360677 _Gus Wiseman_, Mar 05 2023