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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
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
Sequence in context: A117448 A093321 A302015 * A335904 A144736 A137423
KEYWORD
nonn
AUTHOR
STATUS
approved

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