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

1,2

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

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.

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]

Crossrefs

Subsequence of A005117 and A274546.

Cf. A056911, A261034, A366640.

Sequence in context: A024561 A350573 A274546 * A113545 A056825 A070757

Adjacent sequences: A366638 A366639 A366640 * A366642 A366643 A366644

Keyword

nonn,easy

Author

Amiram Eldar, Oct 15 2023

Status

approved