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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|.
3
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.
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 22 2021
STATUS
approved