A366531 Sum of even prime indices of n.

0, 0, 2, 0, 0, 2, 4, 0, 4, 0, 0, 2, 6, 4, 2, 0, 0, 4, 8, 0, 6, 0, 0, 2, 0, 6, 6, 4, 10, 2, 0, 0, 2, 0, 4, 4, 12, 8, 8, 0, 0, 6, 14, 0, 4, 0, 0, 2, 8, 0, 2, 6, 16, 6, 0, 4, 10, 10, 0, 2, 18, 0, 8, 0, 6, 2, 0, 0, 2, 4, 20, 4, 0, 12, 2, 8, 4, 8, 22, 0, 8, 0, 0, 6

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.

Examples

			The prime indices of 198 are {1,2,2,5}, so a(198) = 2+2 = 4.
		

Crossrefs

Zeros are A066208, counted by A000009.

The triangle for the odd version is A113685, without zeros A365067.

The triangle for this statistic is A113686, without zeros A174713.

The odd version is A366528.

The halved version is A366533.

A066207 lists numbers with all even prime indices, counted by A035363.

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

A239261 counts partitions with sum of odd parts = sum of even parts.

A257991 counts odd prime indices, even A257992.

A346697 adds up odd-indexed prime indices, even-indexed A346698.

A366322 lists numbers with not all prime indices even, counted by A086543.

Cf. A000720, A055396, A055922, A061395, A162641, A171966, A258117, A325698, A325700, A352140, A352141.

Programs

Mathematica

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

Formula

a(n) = A056239(n) - A366528(n).