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

1,2

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.

Links

Table of n, a(n) for n=1..67.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

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

Example

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

Mathematica

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

Crossrefs

See link for additional cross-references.

Complement of A327407.

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

Sequence in context: A183221 A317492 A324721 * A305732 A265999 A316502

Adjacent sequences: A327531 A327532 A327533 * A327535 A327536 A327537

Keyword

nonn

Author

Gus Wiseman, Sep 17 2019

Status

approved