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

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, 1216, 8, 64, 16, 872, 24, 160, 8, 532, 52, 120, 12, 424, 100, 24, 4, 8, 944, 24, 144, 12, 1912, 272, 8, 16, 276, 24, 64, 144, 1856, 20, 96, 1276, 40, 112, 12, 8, 116, 20, 16, 96, 8

Offset: 1

Author

T. D. Noe, Aug 13 2008

Keywords

• nonn

Comments

a(n) is the number of divisors of A143407(n) that are not divisors of A143407(r) for r

Examples

			Because A002174(5)=8 and psi(k)=8 for k=32,96,160,480, we have a(5)=4.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..500
• P. J. Cameron and D. A. Preece, Notes on primitive lambda-roots, 2009. See formula in theorem 5.2 (c) p. 8.

Crossrefs

Cf. A002322 (reduced totient function), A079612.

Programs

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;);}
nb(n) = sumdiv(n, d, moebius(n/d)*numdiv(a079612(d)));
lista(nn) = for (n=1, nn, if (nbs = nb(n), print1(nbs, ", "))); \\ Michel Marcus, May 12 2018

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