%I #14 Dec 16 2017 22:41:43

%S 0,0,0,1,0,2,0,2,1,2,0,3,0,3,2,2,0,4,0,4,3,4,0,5,1,4,2,4,0,6,0,5,3,5,

%T 2,6,0,5,3,6,0,8,0,6,5,6,0,9,2,7,4,6,0,9,4,7,5,7,0,11,0,8,7,7,3,10,0,

%U 8,5,10,0,11,0,10,9,10,4,12,0,11,6,10,0,14,5,10,7,11,0,15,4,10,7,10,4,13,0

%N Number of primes between n and phi(n), with neither n nor phi(n) included in the count in case they are primes.

%H Antti Karttunen, <a href="/A074398/b074398.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A085342(n) - A010051(n) = A000720(n) - A000720(A000010(n)) - A010051(n). - _Antti Karttunen_, Dec 16 2017

%e phi(6) = 2 and there are 2 primes between 2 and 6 (endpoints are excluded), namely 3, 5. Hence a(6) = 2.

%t (*gives number of primes < n*) f[n_] := Module[{r, i}, r = 0; i = 1; While[Prime[i] < n, i++ ]; i - 1]; (*gives number of primes between m and n with endpoints excluded*) g[m_, n_] := Module[{r}, r = f[m] - f[n]; If[PrimeQ[n], r = r - 1]; r]; Table[g[n, EulerPhi[n]], {n, 1, 100}]

%t (* Second program: *)

%t Array[PrimePi@ # - PrimePi@ EulerPhi@ # - Boole@ PrimeQ@ # &, 96] (* or *) Array[Count[Range[EulerPhi@ # + 1, # - 1], _?PrimeQ] &, 96] (* _Michael De Vlieger_, Dec 16 2017 *)

%o (PARI) A074398(n) = (primepi(n) - primepi(eulerphi(n)) - isprime(n)); \\ _Antti Karttunen_, Dec 16 2017

%Y Cf. A000010, A000720, A010051, A085342.

%K nonn,look

%O 1,6

%A _Joseph L. Pe_, Sep 24 2002

%E Name clarified by _Antti Karttunen_, Dec 16 2017