%I #11 Feb 16 2025 08:33:01

%S 1,3,7,11,19,23,35,43,51,59,79,87,111,123,139,153,185,197,233,247,271,

%T 291,335,351,377,401,427,445,501,517,577,603,643,675,723,745,817,853,

%U 901,929,1009,1033,1117,1151,1187,1231,1323,1353,1405,1439,1503,1541

%N Number of weakly carefree couples (a,b) with a,b<=n.

%C (a, b) is a weakly carefree couple if gcd(a, b) = 1 and either a or b is squarefree (A005117). - _Amiram Eldar_, Mar 03 2021

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.5.1 Carefree Couples, p. 110.

%H Pieter Moree, <a href="https://arxiv.org/abs/math/0510003">Counting carefree couples</a>, arXiv:math/0510003 [math.NT], 2005-2014.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CarefreeCouple.html">Carefree Couple</a>.

%F From _Amiram Eldar_, Mar 03 2021: (Start)

%F a(n) = 2*A118258(n) - A118259(n).

%F a(n) ~ A118261 * n^2 + O(n*log(n)). (End)

%Y Cf. A005117, A118258, A118259, A118261.

%K nonn,changed

%O 1,2

%A _Eric W. Weisstein_, Apr 20 2006