A366849 Odd numbers whose halved even prime indices are relatively prime.

3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 91, 93, 99, 105, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 183, 189, 195, 201, 203, 207, 213, 219, 225, 231, 237, 243, 247, 249, 255, 261, 267, 273, 279, 285, 291, 297, 301, 303, 309

Offset: 1

Author

Gus Wiseman, Nov 01 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 even prime indices of 91 are {4,6}, halved {2,3}, which are relatively prime, so 91 is in the sequence.
The prime indices of 665 are {3,4,8}, even {4,8}, halved {2,4}, which are not relatively prime, so 665 is not in the sequence.
The terms together with their prime indices begin:
   3: {2}
   9: {2,2}
  15: {2,3}
  21: {2,4}
  27: {2,2,2}
  33: {2,5}
  39: {2,6}
  45: {2,2,3}
  51: {2,7}
  57: {2,8}
  63: {2,2,4}
  69: {2,9}
  75: {2,3,3}
  81: {2,2,2,2}
  87: {2,10}
  91: {4,6}
  93: {2,11}
  99: {2,2,5}
		

Crossrefs

For odd instead of halved even prime indices we have A366848.

A version for odd indices A366846, counted by A366850.

This is the odd restriction of A366847, counted by A366845.

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

A035363 counts partitions into all even parts, ranks A066207.

A112798 lists prime indices, length A001222, sum A056239.

A162641 counts even prime exponents, odd A162642.

A257992 counts even prime indices, odd A257991.

A289509 lists numbers with relatively prime prime indices, ones of A289508, counted by A000837.

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, A302697, A325698, A366842, A366843.

Programs

Mathematica

Select[Range[100], OddQ[#]&&GCD@@Select[PrimePi/@First/@FactorInteger[#], EvenQ]==2&]