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 A231772 Smallest positive number which has exactly n primitive roots, or 0 if no such number exists. 2
 8, 1, 5, 0, 11, 0, 19, 0, 17, 0, 23, 0, 29, 0, 0, 0, 41, 0, 81, 0, 67, 0, 47, 0, 53, 0, 0, 0, 59, 0, 0, 0, 97, 0, 0, 0, 109, 0, 0, 0, 83, 0, 0, 0, 139, 0, 0, 0, 113, 0, 0, 0, 107, 0, 163, 0, 0, 0, 0, 0, 199, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS If n >= 3 and n is odd, then a(n) = 0. LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Primitive Root MATHEMATICA nn = 100; t = Join[{1}, Table[p = PrimitiveRoot[n]; If[IntegerQ[p], EulerPhi[EulerPhi[n]], 0], {n, 2, 2*nn}]]; Table[s = Position[t, n, 1, 1]; If[s == {}, 0, s[[1, 1]]], {n, 0, nn}] (* T. D. Noe, Nov 14 2013 *) PROG (PARI) r=77; print1(8, ", ", 1, ", "); for(n=2, r, m=0; for(c=2*n+1, n^2+1, if(n%2==1, break); e=eulerphi(c); if(e==lcm(znstar(c)[2])&&eulerphi(e)==n, m=1; print1(c, ", "); break)); if(m==0, print1(0, ", "))); CROSSREFS Cf. A007617, A010554, A046144, A231773. Sequence in context: A163898 A280040 A202284 * A338935 A200120 A154861 Adjacent sequences:  A231769 A231770 A231771 * A231773 A231774 A231775 KEYWORD nonn AUTHOR Arkadiusz Wesolowski, Nov 13 2013 STATUS approved

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Last modified September 18 01:39 EDT 2021. Contains 347504 sequences. (Running on oeis4.)