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A212552
Smallest prime factor of p^p - 1 that is congruent to 1 modulo p where p = prime(n).
4
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
1,1
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
EXAMPLE
a(4) = 29 because prime(4) = 7 and 7^7 -1 = 823542 = 2 * 3 * 29 * 4733 => 29 == 1 (mod 7).
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}]
CROSSREFS
Cf. A187023.
Sequence in context: A273576 A272849 A273613 * A272938 A273649 A272994
KEYWORD
nonn
AUTHOR
Michel Lagneau, May 20 2012
STATUS
approved