A366848 Odd numbers whose odd prime indices are relatively prime.

55, 85, 155, 165, 187, 205, 253, 255, 275, 295, 335, 341, 385, 391, 415, 425, 451, 465, 485, 495, 527, 545, 561, 595, 605, 615, 635, 649, 697, 713, 715, 737, 745, 759, 765, 775, 785, 799, 803, 825, 885, 895, 913, 935, 943, 955, 1003, 1005, 1023, 1025, 1045

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 odd prime indices of 345 are {3,9}, which are not relatively prime, so 345 is not in the sequence.
The odd prime indices of 825 are {3,3,5}, which are relatively prime, so 825 is in the sequence
The terms together with their prime indices begin:
    55: {3,5}
    85: {3,7}
   155: {3,11}
   165: {2,3,5}
   187: {5,7}
   205: {3,13}
   253: {5,9}
   255: {2,3,7}
   275: {3,3,5}
   295: {3,17}
   335: {3,19}
   341: {5,11}
   385: {3,4,5}
   391: {7,9}
   415: {3,23}
   425: {3,3,7}
   451: {5,13}
   465: {2,3,11}
   485: {3,25}
   495: {2,2,3,5}
		

Crossrefs

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

Including even prime indices gives A302697, counted by A302698.

Including even terms gives A366846, counted by A366850.

For halved even instead of odd prime indices we have A366849.

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

A066208 lists numbers with all odd prime indices, even A066207.

A112798 lists prime indices, length A001222, sum A056239.

A257991 counts odd prime indices, even A257992.

A366528 adds up odd prime indices, partition triangle A113685.

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

Cf. A000720, A018783, A055396, A061395, A087436, A325698, A365067, A366842, A366843, A366844, A366847.

Programs

Mathematica

Select[Range[1000], OddQ[#]&&GCD@@Select[PrimePi/@First/@FactorInteger[#], OddQ]==1&]