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%I #26 Nov 05 2022 08:18:51
%S 1,3,12,12,30,36,56,48,108,90,132,144,182,168,360,192,306,324,380,360,
%T 672,396,552,576,750,546,972,672,870,1080,992,768,1584,918,1680,1296,
%U 1406,1140,2184,1440,1722,2016,1892,1584,3240,1656,2256,2304,2744,2250
%N Size of largest conjugacy class in the group GL(2,Z_n).
%H Amiram Eldar, <a href="/A070732/b070732.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = (p+1)*p^(2e - k), k = 1 if p is odd, k = 2 if p is 2.
%F a(n) = A000056(n)/A000010(2*n). - _Vladeta Jovovic_, Dec 22 2003
%F From _R. J. Mathar_, Apr 14 2011: (Start)
%F Dirichlet g.f.: (2^s-1)*zeta(s-1)*zeta(s-2)/((2^s+2)*zeta(2s-2)).
%F Dirichlet convolution of A000082 with a signed variant of A099892. (End)
%F Sum_{k=1..n} a(k) ~ 7*n^3 / (2*Pi^2). - _Vaclav Kotesovec_, Feb 01 2019
%F Sum_{n>=1} 1/a(n) = (13/11) * zeta(2)^2 * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 1/p^4) = (13/11) * A098198 * A330523 = 1.7136743536... . - _Amiram Eldar_, Nov 05 2022
%t f[n_] := Block[{a = 1, b = FactorInteger[n]}, While[ Length[b] > 0, a = a*(b[[1, 1]] + 1)*b[[1, 1]]^(2b[[1, 2]] - If[ OddQ[ b[[1, 1]]], 1, 2]); b = Drop[b, 1]]; a]; Table[ f[n], {n, 1, 55}]
%t Table[n*Sum[d^2 MoebiusMu[n/d], {d, Divisors[n]}]/EulerPhi[2*n], {n, 1, 100}] (* _Vaclav Kotesovec_, Feb 01 2019 *)
%t f[p_, e_] := (p + 1)*p^(2*e - If[p == 2, 2, 1]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 14 2020 *)
%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i,1]+1)*f[i,1]^(2*f[i,2] - if(f[i,1]==2,2,1)));} \\ _Amiram Eldar_, Nov 05 2022
%Y Cf. A062354.
%Y Cf. A000010, A000056.
%Y Cf. A000082, A099892, A098198, A330523.
%K nonn,mult,easy
%O 1,2
%A Sharon Sela (sharonsela(AT)hotmail.com), May 14 2002
%E Edited by _Robert G. Wilson v_, May 20 2002
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