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 A355658 Smallest prime base q such that q^(p-1) == 1 (mod p^2), where p = prime(n). 0

%I #8 Jul 17 2022 10:51:36

%S 5,17,7,19,3,19,131,127,263,41,229,691,313,19,53,521,53,601,1301,11,

%T 619,31,269,3187,53,181,43,317,499,373,911,659,19,3659,313,751,233,

%U 4373,3307,419,2591,313,1249,2897,349,709,331,1973,1933,503,821,977,2371,263

%N Smallest prime base q such that q^(p-1) == 1 (mod p^2), where p = prime(n).

%C a(n) differs from A125636(n) if and only if p is a Wieferich prime (A001220). In particular, a(183) = 2 and A125636(183) = 18979. Similarly, a(490) = 2 and A125636(490) = 82183.

%o (PARI) a(n) = my(p=prime(n)); forprime(q=1, , if(Mod(q, p^2)^(p-1)==1, return(q)))

%Y Cf. A001220, A125636, A039678.

%K nonn

%O 1,1

%A _Felix FrÃ¶hlich_, Jul 12 2022

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Last modified September 25 05:35 EDT 2023. Contains 365582 sequences. (Running on oeis4.)