A212552 Smallest prime factor of p^p - 1 that is congruent to 1 modulo p where p = prime(n).

3, 13, 11, 29, 15797, 53, 10949, 109912203092239643840221, 461, 59, 568972471024107865287021434301977158534824481, 149, 83, 173, 1693, 107, 709, 977, 269, 105649, 293, 317, 2657, 179, 389, 607, 1237, 137122213, 2617, 227, 509, 1049, 1097, 557, 1193, 2417, 86351

Offset: 1

Author

Michel Lagneau, May 20 2012

Keywords

• nonn

Comments

Subset of A187023.

If p is a prime, then p^p-1 has at least a prime factor that is congruent to 1 modulo p.

Also smallest prime factor of (p^p - 1)/(p - 1). - Jianing Song, Nov 03 2019

Examples

			a(4) = 29 because prime(4) = 7 and 7^7 -1 = 823542 = 2 * 3 * 29 * 4733 => 29 == 1 (mod 7).
		

Crossrefs

Cf. A187023.

Programs

Maple

with(numtheory): for n from 1 to 34 do:i:=0:p:=ithprime(n):x:=p^p -1:y:=factorset(x):n1:=nops(y):for k from 1 to n1 while(i=0) do:z:=y[k]:if irem(z,p)=1 then i:=1: printf ( "%d %d \n",n,z):else fi:od:od:

Mathematica

Table[p=First/@FactorInteger[Prime[n]^Prime[n]-1]; Select[p, Mod[#1, Prime[n]] == 1 &, 1][[1]], {n, 1, 10}]