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A098243
Numbers having the same number of primitive roots that are primes == 1 or 2 (mod 4) as primes == 3 (mod 4).
0
5, 7, 11, 14, 18, 22, 27, 31, 41, 43, 49, 50, 53, 54, 62, 73, 81, 101, 146, 166, 179, 206, 211, 227, 250, 317, 461, 478, 614, 811, 911, 961, 974, 1063, 1198, 1237, 1399, 1499, 1693, 1874, 1879, 2161, 2182, 2197, 2207, 2311, 2381, 2473, 2498, 2549, 2594, 2699
OFFSET
1,1
COMMENTS
2 is counted with the primes 1 (mod 4) because it is a frequent prime primitive root and primes (1,2) (mod 4) together build sequence A002313.
EXAMPLE
31 has primitive roots 3, 11, 12, 13, 17, 21, 22, 24, ...;
13 and 17 are primes 1 (mod 4), count is 2;
3 and 11 are primes 3 (mod 4), count is 2;
thus 31 is a term of this sequence.
MATHEMATICA
q[n_] := Module[{p = Select[PrimitiveRootList[n], PrimeQ], m}, m = Length[p]; m > 0 && EvenQ[m] && Length @ Select[p, Mod[#, 4] == 3 &] == m/2]; Select[Range[2700], q] (* Amiram Eldar, Aug 26 2021 *)
CROSSREFS
Cf. A002313.
Sequence in context: A181494 A125293 A354164 * A037141 A355013 A029624
KEYWORD
nonn
AUTHOR
Sven Simon, Aug 31 2004
EXTENSIONS
Offset 1 and name edited by Michel Marcus, Aug 25 2021
STATUS
approved