cp's OEIS Frontend

A085342 Number of primes between phi(n) and n, where n is included in the count if it is a prime, while phi(n) is never included in the count even if it is a prime.

%I A085342 #19 Dec 17 2017 03:05:29
%S A085342 0,1,1,1,1,2,1,2,1,2,1,3,1,3,2,2,1,4,1,4,3,4,1,5,1,4,2,4,1,6,1,5,3,5,
%T A085342 2,6,1,5,3,6,1,8,1,6,5,6,1,9,2,7,4,6,1,9,4,7,5,7,1,11,1,8,7,7,3,10,1,
%U A085342 8,5,10,1,11,1,10,9,10,4,12,1,11,6,10,1,14,5,10,7,11,1,15,4,10,7,10,4,13,1
%N A085342 Number of primes between phi(n) and n, where n is included in the count if it is a prime, while phi(n) is never included in the count even if it is a prime.
%C A085342 Number of primes in (phi(n), n]. - _Charles R Greathouse IV_, Dec 26 2013
%H A085342 Antti Karttunen, <a href="/A085342/b085342.txt">Table of n, a(n) for n = 1..16384</a>
%F A085342 a(n) = pi(n) - pi(phi(n)) = A000720(n) - A000720(A000010(n)).
%F A085342 a(n) = A074398(n) + A010051(n). - _Antti Karttunen_, Dec 16 2017
%e A085342 n=12: phi(n)=4, pi(12)-pi(4)=5-2=3.
%t A085342 Array[PrimePi[#] - PrimePi@ EulerPhi@ # &, 97] (* _Michael De Vlieger_, Dec 16 2017 *)
%o A085342 (PARI) a(n) = primepi(n) - primepi(eulerphi(n)); \\ _Michel Marcus_, Dec 26 2013
%Y A085342 Cf. A000720, A000010, A010051, A070803, A070804, A074398, A085341-A085347.
%K A085342 nonn,look
%O A085342 1,6
%A A085342 _Labos Elemer_, Jul 10 2003
%E A085342 Name clarified by _Antti Karttunen_, Dec 16 2017