A366528 Sum of odd prime indices of n.

0, 1, 0, 2, 3, 1, 0, 3, 0, 4, 5, 2, 0, 1, 3, 4, 7, 1, 0, 5, 0, 6, 9, 3, 6, 1, 0, 2, 0, 4, 11, 5, 5, 8, 3, 2, 0, 1, 0, 6, 13, 1, 0, 7, 3, 10, 15, 4, 0, 7, 7, 2, 0, 1, 8, 3, 0, 1, 17, 5, 0, 12, 0, 6, 3, 6, 19, 9, 9, 4, 0, 3, 21, 1, 6, 2, 5, 1, 0, 7, 0, 14, 23, 2

Offset: 1

Author

Gus Wiseman, Oct 22 2023

Keywords

• nonn

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, sum A056239(n).

Examples

			The prime indices of 198 are {1,2,2,5}, so a(198) = 1+5 = 6.
		

Crossrefs

Zeros are A066207, counted by A035363.

The triangle for this rank statistic is A113685, without zeros A365067.

For count instead of sum we have A257991, even A257992.

Nonzeros are A366322, counted by A086543.

The even version is A366531, halved A366533, triangle A113686.

A000009 counts partitions into odd parts, ranks A066208.

A053253 = partitions with all odd parts and conjugate parts, ranks A352143.

A066967 adds up sums of odd parts over all partitions.

A112798 lists prime indices, reverse A296150, length A001222, sum A056239.

A162641 counts even prime exponents, odd A162642.

A352142 = odd indices with odd exponents, counted by A117958.

Cf. A000720, A055396, A130780, A171966, A174713, A325698, A325700, A366748.

Programs

Mathematica

Table[Total[Cases[FactorInteger[n], {p_?(OddQ@*PrimePi),k_}:>PrimePi[p]*k]],{n,100}]

Formula

a(n) = A056239(n) - A366531(n).