A366641 Squarefree numbers that are coprime to the terms of A366640.

1, 2, 3, 6, 7, 11, 13, 14, 17, 19, 21, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 66, 67, 69, 71, 73, 74, 77, 78, 82, 83, 86, 87, 89, 91, 93, 94, 97, 101, 102, 103, 106, 107, 109, 111, 113, 114, 118, 119, 122, 123, 127

Offset: 1

Author

Amiram Eldar, Oct 15 2023

Keywords

• nonn
• easy

Comments

First differs from A274546 at n = 42.

The asymptotic density of this sequence is 1/2.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A005117 and A274546.

Cf. A056911, A261034, A366640.

Programs

Mathematica

seq[max_] := With[{ps = {5, 79, 1831}}, If[max <= Max[ps], Select[Range[max], And @@ CoprimeQ[#, ps] && SquareFreeQ[#] &], Print["Add to ps more terms from A366640"]]]; seq[130]

Formula

a(n) ~ 2*n.

Sum_{n>=1} 1/a(n)^s = (zeta(s)/zeta(2*s)) / Product_{p in A366640} (1 + 1/p^s), s>1.