A098243 Numbers having the same number of primitive roots that are primes == 1 or 2 (mod 4) as primes == 3 (mod 4).

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.

Links

Table of n, a(n) for n=1..52.

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

Adjacent sequences: A098240 A098241 A098242 * A098244 A098245 A098246

Keyword

nonn

Author

Sven Simon, Aug 31 2004

Extensions

Offset 1 and name edited by Michel Marcus, Aug 25 2021

Status

approved