A366846 Numbers whose odd prime indices are relatively prime.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 55, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 85, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122

Offset: 1

Author

Gus Wiseman, Oct 29 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 odd prime indices of 115 are {3,9}, and these are not relatively prime, so 115 is not in the sequence.
The odd prime indices of 825 are {3,3,5}, and these are relatively prime, so 825 is in the sequence.
		

Crossrefs

Including even indices gives A289509, ones of A289508, counted by A000837.

The complement when including even indices is A318978, counted by A018783.

The nonzero complement ranks the partitions counted by A366842.

The version for halved even indices is A366847.

The odd case is A366848.

The partitions with these Heinz numbers are counted by A366850.

A000041 counts integer partitions, strict A000009 (also into odds).

A112798 lists prime indices, length A001222, sum A056239.

A257992 counts even prime indices, odd A257991.

A366528 adds up odd prime indices, partition triangle A113685.

A366531 = 2*A366533 adds up even prime indices, triangle A113686/A174713.

Cf. A000720, A055396, A061395, A066208, A087436, A302696, A302697, A325698, A366843, A366844, A366849.

Programs

Mathematica

Select[Range[100], GCD@@Select[PrimePi/@First/@FactorInteger[#], OddQ]==1&]