A163109 - OEIS

%I #20 Jan 08 2018 01:47:46

%S 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,

%T 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,

%U 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

%N a(n) = phi(tau(n)).

%H Antti Karttunen, <a href="/A163109/b163109.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = A000010(A000005(n)). - _Charles R Greathouse IV_, Aug 11 2009

%F 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).

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

%t Table[EulerPhi[DivisorSigma[0, n]], {n, 1, 80}] (* _Carl Najafi_, Aug 15 2011 *)

%o (PARI) a(n) = eulerphi(numdiv(n)); \\ _Michel Marcus_, Aug 22 2015

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

%K nonn,easy

%O 1,4

%A _Jaroslav Krizek_, Jul 20 2009

%E More terms from _Carl Najafi_, Aug 15 2011

%E Further extended by _Antti Karttunen_, Jul 23 2017