A360676 Sum of the left half (exclusive) of the prime indices of n.

0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 0, 2, 3, 1, 2, 1, 0, 1, 0, 2, 2, 1, 3, 2, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 0, 2, 4, 1, 2, 1, 0, 3, 3, 2, 2, 1, 0, 2, 0, 1, 2, 3, 3, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 4, 1, 0, 2, 4, 1, 0, 2, 3, 1, 2

Offset

1,9

Comments

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.

Links

Table of n, a(n) for n=1..87.

Formula

A360676(n) + A360679(n) = A001222(n).

A360677(n) + A360678(n) = A001222(n).

Example

The prime indices of 810 are {1,2,2,2,2,3}, with left half (exclusive) {1,2,2}, so a(810) = 5.
The prime indices of 3675 are {2,3,3,4,4}, with left half (exclusive) {2,3}, so a(3675) = 5.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Total[Take[prix[n], Floor[Length[prix[n]]/2]]], {n, 100}]

Crossrefs

Positions of 0's are 1 and A000040.

Positions of first appearances are 1 and A001248.

These partitions are counted by A360675, right A360672.

A112798 lists prime indices, length A001222, sum A056239, median* A360005.

A360616 gives half of bigomega (exclusive), inclusive A360617.

A360673 counts multisets by right sum (exclusive), inclusive A360671.

First for prime indices, second for partitions, third for prime factors:

- A360676 gives left sum (exclusive), counted by A360672, product A361200.

- A360677 gives right sum (exclusive), counted by A360675, product A361201.

- A360678 gives left sum (inclusive), counted by A360675, product A347043.

- A360679 gives right sum (inclusive), counted by A360672, product A347044.

Cf. A026424, A280076, A359912, A360006, A360457, A360674.

Sequence in context: A065363 A119995 A062756 * A334107 A346700 A301574

Adjacent sequences: A360673 A360674 A360675 * A360677 A360678 A360679

Keyword

nonn

Author

Gus Wiseman, Mar 04 2023

Status

approved