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A242750
Positive integers n with property that n is a primitive root modulo prime(n).
9
1, 2, 3, 6, 7, 10, 11, 13, 15, 18, 24, 26, 28, 33, 39, 41, 44, 45, 48, 50, 54, 55, 56, 58, 62, 65, 68, 69, 71, 75, 79, 83, 85, 93, 95, 107, 108, 109, 110, 117, 118, 119, 120, 123, 126, 129, 130, 131, 133, 139, 142, 143, 145, 148, 157, 158, 160, 163, 164, 166, 170, 172, 173, 174, 179, 182, 186, 190, 191, 195
OFFSET
1,2
COMMENTS
According to the conjecture in A242748, this sequence should have infinitely many terms.
EXAMPLE
6 is a member since 6 is a primitive root modulo prime(6) = 13, but 4 and 5 are not since 4 is not a primitive root modulo prime(4) = 7 and 5 is not a primitive root modulo prime(5) = 11.
MATHEMATICA
dv[n_]:=Divisors[n]
n=0; Do[Do[If[Mod[k^(Part[dv[Prime[k]-1], j]), Prime[k]]==1, Goto[aa]], {j, 1, Length[dv[Prime[k]-1]]-1}]; n=n+1; Print[n, " ", k]; Label[aa]; Continue, {k, 1, 195}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 21 2014
STATUS
approved