A345426 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, 2, 4, 5, 8, 8, 12, 12, 14, 15, 21, 14, 20, 20, 22, 24, 23, 14, 25, 16, 19, 23, 39, 11, 5, 4, -3, 6, 20, 8, 24, -10, -19, -10, -22, -43, -30, -44, -43, -47, -39, -92, -38, -51, -61, -55, -57, -127, -174, -163, -152, -171, -176, -188, -165, -167, -197, -186, -177, -298, -228

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..62.

Mathematica

T[x_, y_] := T[x, y] = Module[{u, v}, MinimalBy[{u, v} /. Solve[u^2 + v^2 <= x^2 + y^2 && u*x + v*y == GCD[x, y], {u, v}, Integers], #.# &]];
a[n_] := a[n] = Sum[T[x, y][[1, 1]], {x, 1, n}, {y, 1, n}];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 62}] (* Jean-François Alcover, Mar 28 2023 *)

Prog

(Python)
from sympy.core.numbers import igcdex
def A345426(n): return sum(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, Jul 01 2021

Crossrefs

Cf. A345415-A345428.

Sequence in context: A085624 A331376 A369601 * A061884 A286002 A029935

Adjacent sequences: A345423 A345424 A345425 * A345427 A345428 A345429

Keyword

sign

Author

N. J. A. Sloane, Jun 22 2021

Status

approved