A360679 Sum of the right half (inclusive) of the prime indices of n.

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, 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, 3, 6, 7, 19, 8, 9, 7, 20, 5, 21, 12, 6, 9, 5, 8, 22, 5, 4

Offset

1,3

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..81.

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 right half (inclusive) {2,2,3}, so a(810) = 7.
The prime indices of 3675 are {2,3,3,4,4}, with right half (inclusive) {3,4,4}, so a(3675) = 11.

Mathematica

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

Crossrefs

Positions of first appearances are 1 and A001248.

The value k appears A360671(k) times, exclusive A360673.

These partitions are counted by A360672 with rows reversed.

The exclusive version is A360677.

The left version is A360678.

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

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

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, A359912, A360006, A360007, A360457.

Sequence in context: A123021 A317056 A346699 * A339894 A355140 A286632

Adjacent sequences: A360676 A360677 A360678 * A360680 A360681 A360682

Keyword

nonn

Author

Gus Wiseman, Mar 05 2023

Status

approved