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%I #11 Mar 25 2017 14:25:41
%S 0,1,2,4,9,10,12,72,112,33,12,212,42,22,108,96,35,456,6,1912,714,220,
%T 60,5364,4032,747,448,3944,762,24370,8,5376,738,8148,996,253568,1143,
%U 242,980,46032,248,65138,56,23004,195768,282,28,386736,327520,12102,24366
%N Number of moduli m such that the multiplicative order of n mod m equals n.
%F a(n) = |{m : multiplicative order of n mod m = n}|.
%F a(n) = Sum_{d|n} mu(n/d)*tau(n^d-1), mu = A008683, tau = A000005.
%p with(numtheory):
%p a:= n-> add(mobius(n/d)*tau(n^d-1), d=divisors(n)):
%p seq(a(n), n=1..30);
%t a[n_] := DivisorSum[n, MoebiusMu[n/#]*DivisorSigma[0, n^#-1]&]; a[1] = 0;
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 46}] (* _Jean-François Alcover_, Mar 25 2017, translated from Maple *)
%o (PARI) a(n) = if (n==1, 1, sumdiv(n, d, moebius(n/d)*numdiv(n^d-1))); \\ _Michel Marcus_, Mar 25 2017
%Y Main diagonal of A212957.
%Y Cf. A000005, A008683.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Dec 21 2014
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