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A046144
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Number of primitive roots modulo n.
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22
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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
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OFFSET
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1,5
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LINKS
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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.
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FORMULA
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a(n) is equal to A010554(n) unless n is a term of A033949, in which case a(n)=0.
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MAPLE
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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
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MATHEMATICA
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Prepend[ Table[ If[ IntegerQ[ PrimitiveRoot[n]] , EulerPhi[ EulerPhi[n]], 0], {n, 2, 91}], 1] (* Jean-François Alcover, Sep 13 2011 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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