A074398 Number of primes between n and phi(n), with neither n nor phi(n) included in the count in case they are primes.

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, 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, 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

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A085342(n) - A010051(n) = A000720(n) - A000720(A000010(n)) - A010051(n). - Antti Karttunen, Dec 16 2017

Example

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

Mathematica

(*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}]
(* Second program: *)
Array[PrimePi@ # - PrimePi@ EulerPhi@ # - Boole@ PrimeQ@ # &, 96] (* or *) Array[Count[Range[EulerPhi@ # + 1, # - 1], _?PrimeQ] &, 96] (* Michael De Vlieger, Dec 16 2017 *)

Prog

(PARI) A074398(n) = (primepi(n) - primepi(eulerphi(n)) - isprime(n)); \\ Antti Karttunen, Dec 16 2017

Crossrefs

Cf. A000010, A000720, A010051, A085342.

Sequence in context: A068067 A046926 A200815 * A144765 A308062 A147588

Adjacent sequences: A074395 A074396 A074397 * A074399 A074400 A074401

Keyword

nonn,look

Author

Joseph L. Pe, Sep 24 2002

Extensions

Name clarified by Antti Karttunen, Dec 16 2017

Status

approved