A292285 GCD of orders (in GF(p)) of primes dividing p-1, for odd primes p.

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, 53, 9, 14, 7, 65, 68, 46, 37, 5, 2, 162, 83, 43, 89, 15, 19, 16, 98, 11, 35, 37, 113, 19, 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

Offset

2,1

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Seva, Posting on mathoverflow.net, October 29 2014.

Example

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.

Maple

with(numtheory):
a:= n-> (p-> igcd(map(x-> order(x, p), factorset(p-1))[]))(ithprime(n)):
seq(a(n), n=2..100);  # Alois P. Heinz, Dec 01 2017

Mathematica

a[n_] := With[{k = Prime[n]-1}, GCD @@ (MultiplicativeOrder[#, k+1]& /@ FactorInteger[k][[All, 1]])];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Apr 30 2019 *)

Crossrefs

Cf. A172058, A295975.

Sequence in context: A256751 A249484 A134017 * A163984 A283366 A048186

Adjacent sequences: A292282 A292283 A292284 * A292286 A292287 A292288

Keyword

nonn,look

Author

Jeffrey Shallit, Dec 01 2017

Status

approved