A118260 Number of weakly carefree couples (a,b) with a,b<=n.

1, 3, 7, 11, 19, 23, 35, 43, 51, 59, 79, 87, 111, 123, 139, 153, 185, 197, 233, 247, 271, 291, 335, 351, 377, 401, 427, 445, 501, 517, 577, 603, 643, 675, 723, 745, 817, 853, 901, 929, 1009, 1033, 1117, 1151, 1187, 1231, 1323, 1353, 1405, 1439, 1503, 1541

Offset

1,2

Comments

(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

References

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

Links

Table of n, a(n) for n=1..52.

Pieter Moree, Counting carefree couples, arXiv:math/0510003 [math.NT], 2005-2014.

Eric Weisstein's World of Mathematics, Carefree Couple.

Formula

From Amiram Eldar, Mar 03 2021: (Start)

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

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

Crossrefs

Cf. A005117, A118258, A118259, A118261.

Sequence in context: A361562 A277878 A117991 * A018805 A191037 A292083

Adjacent sequences: A118257 A118258 A118259 * A118261 A118262 A118263

Keyword

nonn

Author

Eric W. Weisstein, Apr 20 2006

Status

approved