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A345427
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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 v.
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4
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1, 3, 5, 8, 10, 14, 15, 20, 21, 24, 26, 33, 27, 34, 35, 38, 41, 41, 33, 45, 37, 41, 46, 63, 36, 31, 31, 25, 35, 50, 39, 56, 23, 15, 25, 14, -6, 8, -5, -3, -6, 3, -49, 6, -6, -15, -8, -9, -78, -124, -112, -100, -118, -122, -133, -109, -110, -139, -127, -117, -237, -166, -185, -218, -171, -215
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OFFSET
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1,2
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COMMENTS
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Minimal means minimize u^2+v^2. We follow Maple, PARI, etc., in setting u=0 and v=1 when x=y.
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LINKS
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MATHEMATICA
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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, 2]], {x, 1, n}, {y, 1, n}];
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PROG
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(Python)
from sympy.core.numbers import igcdex
def A345427(n): return sum(v 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
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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