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%I #26 Aug 08 2018 04:31:41
%S 1,4,16,32,32,64,96,192,216,128,240,512,288,384,512,1024,512,864,720,
%T 1024,1536,960,1056,3072,1200,1152,2592,3072,1568,2048,1920,5120,3840,
%U 2048,3072,6912,2592,2880,4608,6144,3200,6144,3696,7680,6912,4224,4416
%N a(n) = Sum_{0 < x,y <= n and gcd(x^2 + y^2, n)=1} gcd(x^2 + y^2 - 1, n).
%C Related to Menon's identity. See Conclusions and further work section of the arXiv file linked.
%C 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
%H Antti Karttunen, <a href="/A239611/b239611.txt">Table of n, a(n) for n = 1..2101</a>
%H C. Calderón, J. M. Grau, A. Oller-Marcen, L. Toth, <a href="http://arxiv.org/abs/1403.7878">Counting invertible sums of squares modulo n and a new generalization of Euler totient function</a>, arXiv:1403.7878 [math.NT], 2014.
%t 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]
%o (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
%Y Cf. A239612, A239613, A239614, A239615, A079458, A053191, A227499, A244342.
%K nonn,mult
%O 1,2
%A _José María Grau Ribas_, Jun 24 2014