A100141 - OEIS

A100141

Numbers n such that the number of prime primitive roots of n is a prime primitive root of n

%I #8 Sep 25 2021 06:50:07

%S 5,9,11,19,23,34,37,38,46,67,94,121,167,178,194,269,274,281,358,382,

%T 457,521,601,625,626,698,709,719,818,839,958,1006,1094,1217,1303,1402,

%U 1439,1453,1493,1502,1579,1601,1663,1706,1838,1871,1901,1913,1922,2011,2066

%N Numbers n such that the number of prime primitive roots of n is a prime primitive root of n

%C A100142(n) gives the number of prime primitive roots of these numbers.

%H Amiram Eldar, <a href="/A100141/b100141.txt">Table of n, a(n) for n = 1..1000</a>

%e 19 has prime primitive roots 2, 3, 13. Count is 3, which is a prime primitive root of 19.

%t q[n_] := Module[{p = Select[PrimitiveRootList[n], PrimeQ], m}, m = Length[p]; MemberQ[p, m] && PrimeQ[m]]; Select[Range[2000], q] (* _Amiram Eldar_, Sep 25 2021 *)

%Y Cf. A100142.

%K easy,nonn

%O 1,1

%A _Sven Simon_, Nov 07 2004

%E a(2) inserted by _Amiram Eldar_, Sep 25 2021