A327534 Numbers that are 1, prime, or whose prime indices are relatively prime.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Offset: 1

Author

Gus Wiseman, Sep 17 2019

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. Numbers whose prime indices are relatively prime are A289509.

Examples

			91 = 7 * 13 has prime indices {4,6}, which have a common divisor of 2, so 91 is not in the sequence.
		

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Complement of A327407.

Cf. A056239, A112798, A281116, A289509, A302569.

Programs

Mathematica

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

Formula

Equals the union of {1}, A000040, and A289509.