A163109 a(n) = phi(tau(n)).

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 6, 1, 2, 2, 4, 1, 4, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 2, 6, 2, 4, 1, 2, 2, 4, 1, 4, 1, 2, 2, 2, 2, 4, 1, 4, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 2, 2, 2, 2, 4, 1, 2, 2, 6, 1, 4, 1, 4, 4

Offset: 1

Author

Jaroslav Krizek, Jul 20 2009

Keywords

• nonn
• easy

Examples

			a(16) = a(2^(5-1)) = 5-1 = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000005, A000010, A062821, A163377, A163378, A163379.

Programs

Mathematica

Table[EulerPhi[DivisorSigma[0, n]], {n, 1, 80}] (* Carl Najafi, Aug 15 2011 *)

PARI

a(n) = eulerphi(numdiv(n)); \\ Michel Marcus, Aug 22 2015

Formula

a(n) = A000010(A000005(n)). - Charles R Greathouse IV, Aug 11 2009

a(1) = 1, a(p) = 1 for p = primes (A000040), a(p*q) = 2 for p*q = product of two distinct primes (A006881), a(p*q*...*z) = 2^(k-1) for p*q*...*z = product of k (k > 2) distinct primes p, q, ..., z (A120944), a(p^(q-1)) = q - 1 for p, q = primes (A000040).

Extensions

More terms from Carl Najafi, Aug 15 2011

Further extended by Antti Karttunen, Jul 23 2017