This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118259 #17 Feb 16 2025 08:33:01
%S A118259 1,3,7,7,13,17,27,27,27,33,47,47,63,73,85,85,107,107,131,131,147,165,
%T A118259 195,195,195,215,215,215,249,265,303,303,329,355,385,385,431,461,495,
%U A118259 495,547,569,625,625,625,661,721,721,721,721,763,763,827,827,877,877
%N A118259 Numbers of strongly carefree couples (a,b) with a,b <= n.
%C A118259 (a, b) is a strongly carefree couple if gcd(a, b) = 1 and both a and b are squarefree (A005117). - _Amiram Eldar_, Mar 03 2021
%D A118259 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.5.1 Carefree Couples, p. 110.
%H A118259 Pieter Moree, <a href="https://arxiv.org/abs/math/0510003">Counting carefree couples</a>, arXiv:math/0510003 [math.NT], 2005-2014.
%H A118259 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CarefreeCouple.html">Carefree Couple</a>.
%F A118259 a(n) = Sum_{i,j=1...n} mu(i*j)^2. - _Benoit Cloitre_, Oct 10 2009
%F A118259 From _Amiram Eldar_, Mar 03 2021: (Start)
%F A118259 a(n) = 2*A118258(n) - A118260(n).
%F A118259 a(n) ~ A065473 * n^2 + O(n*log(n)). (End)
%t A118259 Table[nn = n;Length[Select[Level[Table[Table[{i, j}, {i, 1, nn}], {j, 1, nn}], {2}],Apply[GCD, #] == 1 && SquareFreeQ[#[[1]]] &&SquareFreeQ[#[[2]]] &]], {n, 1, 56}] (* _Geoffrey Critzer_, Jan 13 2015 *)
%o A118259 (PARI) a(n)=sum(i=1,n,sum(j=1,n,moebius(i*j)^2)) \\ _Benoit Cloitre_, Oct 10 2009
%Y A118259 Cf. A005117, A065473, A118258, A118260.
%K A118259 nonn
%O A118259 1,2
%A A118259 _Eric W. Weisstein_, Apr 20 2006