%I #21 Feb 26 2024 01:24:49
%S 2,3,6,7,10,11,14,15,19,23,26,30,34,35,38,39,42,43,46,47,51,55,59,66,
%T 70,71,74,78,79,82,86,91,95,102,106,107,110,111,115,118,119,123,127,
%U 131,134,138,142,143,146,151,154,155,159,167,170,174,178,179,182,186
%N Numbers k such that k, 2*k+1, 3*k+1 are all squarefree.
%C 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
%H Amiram Eldar, <a href="/A062837/b062837.txt">Table of n, a(n) for n = 1..10000</a>
%H Kai-Man Tsang, <a href="https://doi.org/10.1112/S0025579300011049">The distribution of r-tuples of square-free numbers</a>, Mathematika, Vol. 32, No. 2 (1985), pp. 265-275.
%t Select[Range[200],AllTrue[{#,2#+1,3#+1},SquareFreeQ]&] (* _Harvey P. Dale_, Oct 20 2014 *)
%o (PARI) j=[]; for(n=1,200, if(issquarefree(n) && issquarefree(2*n+1) && issquarefree(3*n+1),j=concat(j,n))); j
%Y Subsequence of A005117 and A117204.
%Y Cf. A206256.
%K nonn
%O 1,1
%A _Jason Earls_, Jul 21 2001