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 A046144 Number of primitive roots modulo n. 23
 1, 1, 1, 1, 2, 1, 2, 0, 2, 2, 4, 0, 4, 2, 0, 0, 8, 2, 6, 0, 0, 4, 10, 0, 8, 4, 6, 0, 12, 0, 8, 0, 0, 8, 0, 0, 12, 6, 0, 0, 16, 0, 12, 0, 0, 10, 22, 0, 12, 8, 0, 0, 24, 6, 0, 0, 0, 12, 28, 0, 16, 8, 0, 0, 0, 0, 20, 0, 0, 0, 24, 0, 24, 12, 0, 0, 0, 0, 24, 0, 18, 16, 40, 0, 0, 12, 0, 0, 40, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 S. R. Finch, Idempotents and Nilpotents Modulo n, arXiv:math/0605019 [math.NT], 2006-2017. Eric Weisstein's World of Mathematics, Primitive Root. FORMULA a(n) is equal to A010554(n) unless n is a term of A033949, in which case a(n)=0. MAPLE A046144 := proc(n) local a, eulphi, m; if n = 1 then return 1; end if; eulphi := numtheory[phi](n) ; a := 0 ; for m from 0 to n-1 do if numtheory[order](m, n) = eulphi then a := a + 1 ; end if; end do: a; end proc: # R. J. Mathar, Jan 12 2016 MATHEMATICA Prepend[ Table[ If[ IntegerQ[ PrimitiveRoot[n]] , EulerPhi[ EulerPhi[n]], 0], {n, 2, 91}], 1] (* Jean-François Alcover, Sep 13 2011 *) PROG (PARI) for(i=1, 100, p=0; for(q=1, i, if(gcd(q, i)==1 && znorder(Mod(q, i)) == eulerphi(i), p++)); print1(p, ", ")) /* V. Raman, Nov 22 2012 */ (PARI) a(n) = my(s=znstar(n)); if(#(s.cyc)>1, 0, eulerphi(s.no)) \\ Jeppe Stig Nielsen, Oct 18 2019 (Perl) use ntheory ":all"; my @A = map { !defined znprimroot(\$_) ? 0 : euler_phi(euler_phi(\$_)); } 0..10000; say "\$_ \$A[\$_]" for 1..\$#A; # Dana Jacobsen, Apr 28 2017 CROSSREFS Cf. A001918, A010554, A033949, A046145, A046146, A008330, A002233, A071894, A219027. Sequence in context: A117448 A093321 A302015 * A335904 A144736 A137423 Adjacent sequences: A046141 A046142 A046143 * A046145 A046146 A046147 KEYWORD nonn AUTHOR Eric W. Weisstein STATUS approved

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)