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%I #55 Apr 30 2019 08:24:18
%S 2,4,3,5,3,8,18,11,7,1,18,20,2,23,13,29,10,22,5,3,39,41,11,48,25,17,
%T 53,9,14,7,65,68,46,37,5,2,162,83,43,89,15,19,16,98,11,35,37,113,19,
%U 29,119,8,25,16,131,67,3,23,10,94,73,1,155,39,79,15,7,173,174,88,179,61,62,378,191,97,11,25,51,418,35,43,9,73,17,112,38,23,77
%N GCD of orders (in GF(p)) of primes dividing p-1, for odd primes p.
%H Robert Israel, <a href="/A292285/b292285.txt">Table of n, a(n) for n = 2..10000</a>
%H Seva, <a href="https://mathoverflow.net/questions/185683/why-gcd-rm-ord-pq-colon-q-mid-p-1-likes-to-be-large">Posting on mathoverflow.net</a>, October 29 2014.
%e For n = 14, the 14th prime is 43. The prime divisors of 42 are 2, 3, 7. The orders of 2, 3, 7, respectively, in GF(43), are 14,42,6, with GCD 2.
%p with(numtheory):
%p a:= n-> (p-> igcd(map(x-> order(x, p), factorset(p-1))[]))(ithprime(n)):
%p seq(a(n), n=2..100); # _Alois P. Heinz_, Dec 01 2017
%t a[n_] := With[{k = Prime[n]-1}, GCD @@ (MultiplicativeOrder[#, k+1]& /@ FactorInteger[k][[All, 1]])];
%t Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, Apr 30 2019 *)
%Y Cf. A172058, A295975.
%K nonn,look
%O 2,1
%A _Jeffrey Shallit_, Dec 01 2017
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