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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
OFFSET
0,1
COMMENTS
If n >= 3 and n is odd, then a(n) = 0.
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved