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A143408 Number of numbers k such that the reduced totient function psi(k) = A002174(n).

%I A143408 #9 May 12 2018 16:27:45
%S A143408 2,6,12,16,4,8,84,32,40,32,8,20,20,64,8,480,80,48,12,8,160,20,16,4,8,
%T A143408 1216,8,64,16,872,24,160,8,532,52,120,12,424,100,24,4,8,944,24,144,12,
%U A143408 1912,272,8,16,276,24,64,144,1856,20,96,1276,40,112,12,8,116,20,16,96,8
%N A143408 Number of numbers k such that the reduced totient function psi(k) = A002174(n).
%C A143408 a(n) is the number of divisors of A143407(n) that are not divisors of A143407(r) for r<n.
%H A143408 T. D. Noe, <a href="/A143408/b143408.txt">Table of n, a(n) for n = 1..500</a>
%H A143408 P. J. Cameron and D. A. Preece, <a href="http://www.maths.qmul.ac.uk/~pjc/csgnotes/lambda.pdf">Notes on primitive lambda-roots</a>, 2009. See formula in theorem 5.2 (c) p. 8.
%e A143408 Because A002174(5)=8 and psi(k)=8 for k=32,96,160,480, we have a(5)=4.
%o A143408 (PARI) a079612(n) = {if (n%2, 2, res = 1; forprime(p=2, n+1, if (!(n % (p-1)), t = valuation(n, p); if (p==2, if (t, res *= p^(t+2)), res *= p^(t+1)););); res;);}
%o A143408 nb(n) = sumdiv(n, d, moebius(n/d)*numdiv(a079612(d)));
%o A143408 lista(nn) = for (n=1, nn, if (nbs = nb(n), print1(nbs, ", "))); \\ _Michel Marcus_, May 12 2018
%Y A143408 Cf. A002322 (reduced totient function), A079612.
%K A143408 nonn
%O A143408 1,1
%A A143408 _T. D. Noe_, Aug 13 2008