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 A027413 If n is an odd prime, a(n) = the number of primitive roots mod n, otherwise a(n) =  the number of k < n divisible by at least one but not all of the prime factors of n. 1
 0, 0, 1, 0, 2, 3, 2, 0, 0, 5, 4, 6, 4, 7, 6, 0, 8, 9, 6, 10, 8, 11, 10, 12, 0, 13, 0, 14, 12, 21, 8, 0, 12, 17, 10, 18, 12, 19, 14, 20, 16, 29, 12, 22, 18, 23, 22, 24, 0, 25, 18, 26, 24, 27, 14, 28, 20, 29, 28, 42, 16, 31, 24, 0, 16, 45, 20, 34, 24, 45, 24, 36, 24, 37, 30, 38, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Old name was: "Number of primitive solutions of system "for all 2<=i<=n, k^i > 1 mod n"." The meaning of "primitive" is twofold: (i) Because k^i == (k+n)^i (mod n), we admit only solutions k where k is the representative 2<=k 1 or nops(kimods) = n-1 then             a := a+1 ;         end if;     end do:     a ; end proc: # R. J. Mathar, Jun 09 2016 f:= proc(n) local F, q, r;    if isprime(n) then numtheory:-phi(n-1)    else      F:= numtheory:-factorset(n);      q:= convert(F, `*`);      r:= convert(map(`-`, F, 1), `*`);      n*(q-r-1)/q;     fi; end proc: f(2):= 0: f(1):= 0: map(f, [\$1..1000]); # Robert Israel, Jun 09 2016 MATHEMATICA f[n_] := Module[{F, q, r}, If[PrimeQ[n], EulerPhi[n-1], F = FactorInteger[ n][[All, 1]]; q = Times @@ F; r = Times @@ (F-1); n(q-r-1)/q]]; f[2] = 0; f[1] = 0; f /@ Range[100] (* Jean-François Alcover, Aug 15 2020, after Robert Israel *) CROSSREFS Cf. A000010, A007947, A173557. Sequence in context: A106385 A291293 A259572 * A343230 A019509 A071484 Adjacent sequences:  A027410 A027411 A027412 * A027414 A027415 A027416 KEYWORD nonn AUTHOR Sandor Adrian (sandor(AT)skylab.math.unibuc.ro), Olivier Gérard EXTENSIONS Better definition from Robert Israel, Jun 09 2016 STATUS approved

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Last modified August 4 10:11 EDT 2021. Contains 346447 sequences. (Running on oeis4.)