A345432 For 1<=x<=n, 1<=y<=n, write gcd(x,y) = u*x+v*y with u,v minimal; a(n) = sum of the values of |u|.

0, 1, 4, 8, 17, 24, 42, 58, 82, 104, 149, 177, 240, 286, 340, 404, 512, 579, 714, 799, 910, 1031, 1229, 1341, 1539, 1711, 1918, 2093, 2408, 2574, 2934, 3190, 3478, 3779, 4112, 4362, 4875, 5254, 5662, 5999, 6629, 6969, 7662, 8116, 8593, 9155, 9983, 10431, 11223, 11806

Offset

1,3

Comments

Minimal means minimize u^2+v^2. We follow Maple, PARI, etc., in setting u=0 and v=1 when x=y.

Links

Table of n, a(n) for n=1..50.

Prog

(Python)
from sympy.core.numbers import igcdex
def A345432(n): return sum(abs(u) for u, v, w in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1))) # Chai Wah Wu, Jun 22 2021

Crossrefs

Cf. A345415-A345434.

Sequence in context: A037242 A158139 A026393 * A298950 A213494 A092321

Adjacent sequences: A345429 A345430 A345431 * A345433 A345434 A345435

Keyword

nonn

Author

N. J. A. Sloane, Jun 22 2021

Status

approved