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%I #29 May 05 2021 01:51:26
%S 7,79,6451,2806861
%N Prime numbers p such that p^2 divides 31^(p-1) - 1.
%H Richard Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort.txt">Fermatquotienten von 2 bis 1052</a>, Dec 19 2019.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wieferich_prime">Wieferich prime</a>
%t Select[Range[3*10^6], PrimeQ[#] && PowerMod[31, # - 1, #^2] == 1 &] (* _Amiram Eldar_, May 05 2021 *)
%o (PARI) forprime(p=2, 1e8, if(Mod(31, p^2)^(p-1)==1, print1(p", ")))
%Y Wieferich primes to base b: A001220 (b=2), A014127 (b=3), A123692 (b=5), A123693 (b=7), A128667 (b=13), A128668 (b=17), A090968 (b=19), A128669 (b=23), this sequence (b=31), A331426 (b=37), A331427 (b=41).
%Y Cf. A039951.
%K nonn,more
%O 1,1
%A _Seiichi Manyama_, Jan 16 2020
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