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A163109
a(n) = phi(tau(n)).
12
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
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
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