Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Primes p with the property that no divisor of p-1 is a primitive root modulo p.
1

%I #8 Sep 08 2019 11:48:32

%S 17,41,73,89,97,113,137,193,233,241,251,257,281,307,313,337,353,401,

%T 409,433,439,449,457,499,521,569,577,593,601,617,641,643,673,727,761,

%U 769,809,857,881,919,929,937,953,977,997,1009,1013,1033,1049,1097,1129,1153

%N Primes p with the property that no divisor of p-1 is a primitive root modulo p.

%C The sequence is probably infinite.

%C No element of A001122 nor of A172058 can be in this list.

%H Amiram Eldar, <a href="/A172280/b172280.txt">Table of n, a(n) for n = 1..10000</a>

%t m = 2; t = {}; While[m < bound, m = m + 1; p = Prime[m]; dp = Divisors[p - 1]; L = Length[dp]; j = 1; While[j < L - 1, j = j + 1; b = MultiplicativeOrder[dp[[j]], p]; If[b == p - 1, j = L + 1,] ]; If[j == L + 1, , t = {t, p}] ]; t = Flatten[t]

%Y Cf. A001122 , A172058.

%K easy,nonn

%O 1,1

%A _Emmanuel Vantieghem_, Jan 30 2010