editing

approved

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

approved

editing

proposed

approved

editing

proposed

(Python)

from sympy.core.numbers import igcdex

def A345430(n): return sum(abs(v) for u, v, w in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1)) if w == 1) # Chai Wah Wu, Jun 22 2021

approved

editing

editing

approved

qqqqqv

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

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

Cf. A345415-A345434.

approved

editing

editing

approved

allocated for N. J. A. Sloane

qqqqqv

1, 2, 5, 8, 17, 20, 38, 50, 71, 83, 128, 146, 209, 236, 278, 326, 434, 473, 608, 668, 758, 833, 1031, 1103, 1292, 1400, 1583, 1709, 2024, 2120, 2480, 2672, 2912, 3104, 3410, 3572, 4085, 4328, 4670, 4910, 5540, 5738, 6431, 6761, 7163, 7526, 8354, 8642, 9416, 9788, 10388

1,2

allocated

nonn

N. J. A. Sloane, Jun 22 2021

approved

editing

allocated for N. J. A. Sloane

allocated

approved