A062837 Numbers k such that k, 2*k+1, 3*k+1 are all squarefree.

2, 3, 6, 7, 10, 11, 14, 15, 19, 23, 26, 30, 34, 35, 38, 39, 42, 43, 46, 47, 51, 55, 59, 66, 70, 71, 74, 78, 79, 82, 86, 91, 95, 102, 106, 107, 110, 111, 115, 118, 119, 123, 127, 131, 134, 138, 142, 143, 146, 151, 154, 155, 159, 167, 170, 174, 178, 179, 182, 186

Offset: 1

Author

Jason Earls, Jul 21 2001

Keywords

• nonn

Comments

The asymptotic density of this sequence is (7/3) * Product_{p prime} (1 - 3/p^2) = (7/3) * A206256 = 0.292802955446... (Tsang, 1985). - Amiram Eldar, Feb 26 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Kai-Man Tsang, The distribution of r-tuples of square-free numbers, Mathematika, Vol. 32, No. 2 (1985), pp. 265-275.

Crossrefs

Subsequence of A005117 and A117204.

Cf. A206256.

Programs

Mathematica

Select[Range[200],AllTrue[{#,2#+1,3#+1},SquareFreeQ]&] (* Harvey P. Dale, Oct 20 2014 *)

PARI

j=[]; for(n=1,200, if(issquarefree(n) && issquarefree(2*n+1) && issquarefree(3*n+1),j=concat(j,n))); j