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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

Formula

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A163377 A290085 A322867 * A359289 A286574 A329320

Adjacent sequences: A163106 A163107 A163108 * A163110 A163111 A163112

Keyword

nonn,easy

Author

Jaroslav Krizek, Jul 20 2009

Extensions

More terms from Carl Najafi, Aug 15 2011

Further extended by Antti Karttunen, Jul 23 2017

Status

approved