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

1,1

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..56.

Example

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}

Mathematica

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

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.

Sequence in context: A299790 A030594 A032676 * A228935 A016945 A222640

Adjacent sequences: A366846 A366847 A366848 * A366850 A366851 A366852

Keyword

nonn

Author

Gus Wiseman, Nov 01 2023

Status

approved