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A074398
Number of primes between n and phi(n), with neither n nor phi(n) included in the count in case they are primes.
2
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
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
KEYWORD
nonn,look
AUTHOR
Joseph L. Pe, Sep 24 2002
EXTENSIONS
Name clarified by Antti Karttunen, Dec 16 2017
STATUS
approved