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 A046145 Smallest primitive root modulo n, or 0 if no root exists. 25
 0, 0, 1, 2, 3, 2, 5, 3, 0, 2, 3, 2, 0, 2, 3, 0, 0, 3, 5, 2, 0, 0, 7, 5, 0, 2, 7, 2, 0, 2, 0, 3, 0, 0, 3, 0, 0, 2, 3, 0, 0, 6, 0, 3, 0, 0, 5, 5, 0, 3, 3, 0, 0, 2, 5, 0, 0, 0, 3, 2, 0, 2, 3, 0, 0, 0, 0, 2, 0, 0, 0, 7, 0, 5, 5, 0, 0, 0, 0, 3, 0, 2, 7, 2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 5, 3, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The value 0 at index 0 says 0 has no primitive roots, but the 0 at index 1 says 1 has a primitive root of 0, the only real 0 in the sequence. a(n) is nonzero if and only if n is 2, 4, or of the form p^k, or 2*p^k where p is an odd prime and k>0. - Tom Edgar, Jun 02 2014 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Primitive Root. MAPLE A046145 := proc(n)   if n <=1 then     0;   else     pr := numtheory[primroot](n) ;     if pr = FAIL then        return 0 ;     else        return pr ;     end if;   end if; end proc: seq(A046145(n), n=0..110) ;  # R. J. Mathar, Jul 08 2010 MATHEMATICA smallestPrimitiveRoot[n_ /; n <= 1] = 0; smallestPrimitiveRoot[n_] := Block[{pr = PrimitiveRoot[n], g}, If[! NumericQ[pr], g = 0, g = 1; While[g <= pr, If[ CoprimeQ[g, n] && MultiplicativeOrder[g, n] == EulerPhi[n], Break[]]; g++]]; g]; smallestPrimitiveRoot /@ Range[0, 100] (* Jean-François Alcover, Feb 15 2012 *) f[n_] := Block[{pr = PrimitiveRootList[n]}, If[pr == {}, 0, pr[[1]]]]; Array[f, 105, 0] (* v10.0 Robert G. Wilson v, Nov 04 2014 *) PROG (PARI) { A046145(n) = for(q=1, n-1, if(gcd(q, n)==1 && znorder(Mod(q, n))==eulerphi(n), return(q); )); 0; } /* V. Raman, Nov 22 2012, edited by Max Alekseyev, Apr 20 2017 */ (Perl) use ntheory ":all"; say "\$_ ", znprimroot(\$_) || 0  for 0..100; # Dana Jacobsen, Mar 16 2017 CROSSREFS Cf. A001918, A046144, A046146, A002233, A071894, A219027, A008330, A010554, A111076, A285512, A285513, A285514. Sequence in context: A118176 A005731 A132962 * A103309 A248207 A174621 Adjacent sequences:  A046142 A046143 A046144 * A046146 A046147 A046148 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Initial terms corrected by Harry J. Smith, Jan 27 2005 STATUS approved

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Last modified June 14 12:26 EDT 2021. Contains 345025 sequences. (Running on oeis4.)