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A239611
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a(n) = Sum_{0 < x,y <= n and gcd(x^2 + y^2, n)=1} gcd(x^2 + y^2 - 1, n).
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5
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1, 4, 16, 32, 32, 64, 96, 192, 216, 128, 240, 512, 288, 384, 512, 1024, 512, 864, 720, 1024, 1536, 960, 1056, 3072, 1200, 1152, 2592, 3072, 1568, 2048, 1920, 5120, 3840, 2048, 3072, 6912, 2592, 2880, 4608, 6144, 3200, 6144, 3696, 7680, 6912, 4224, 4416
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OFFSET
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1,2
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COMMENTS
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Related to Menon's identity. See Conclusions and further work section of the arXiv file linked.
Multiplicative by the Chinese remainder theorem since gcd(x, m*n) = gcd(x, m)*gcd(x, n) for gcd(m, n) = 1. - Andrew Howroyd, Aug 07 2018
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LINKS
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MATHEMATICA
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g2[n_] := Sum[If[GCD[x^2 + y^2, n] == 1, GCD[x^2 + y^2 - 1, n], 0], {x, 1, n}, {y, 1, n}]; Array[g2, 100]
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PROG
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(PARI) a(n) = {s = 0; for (x=1, n, for (y=1, n, if (gcd(x^2+y^2, n) == 1, s += gcd(x^2+y^2-1, n)); ); ); s; } \\ Michel Marcus, Jun 29 2014
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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