A383008 Indices of the even terms in the sequence of squarefree numbers.

2, 5, 7, 10, 15, 17, 19, 22, 25, 28, 30, 36, 39, 41, 44, 47, 49, 51, 54, 59, 63, 66, 69, 72, 74, 76, 80, 83, 85, 88, 91, 94, 97, 102, 104, 106, 108, 111, 114, 116, 119, 124, 127, 129, 132, 135, 138, 140, 143, 148, 151, 156, 159, 161, 164, 169, 171, 173, 176, 178

Offset: 1

Author

Amiram Eldar, Apr 12 2025

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is 1/3.

Links

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

Crossrefs

Cf. A005117, A039956, A071403, A373550, A383009.

Programs

Mathematica

Position[Select[Range[350], SquareFreeQ], _?EvenQ] // Flatten

PARI

list(lim) = {my(c = 0); for(k = 1, lim, if(issquarefree(k), c++; if(!(k % 2), print1(c, ", "))));}

Formula

A005117(a(n)) = A039956(n).

A373550(a(n)) = 0.