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%I #28 Feb 14 2017 09:23:29
%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 odd prime base q such that p^2 divides q^(p-1) - 1, where p = prime(n).
%H Robert Israel, <a href="/A125636/b125636.txt">Table of n, a(n) for n = 1..1000</a>
%H W. Keller and J. Richstein, <a href="http://web.archive.org/web/20091109011757/http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients that are divisible by p</a>.
%p a:= proc(p)
%p local q;
%p q:= 3;
%p while (q &^ (p-1) - 1) mod p^2 <> 0 do
%p q:= nextprime(q)
%p od:
%p q
%p end proc:
%p seq(a(ithprime(n)), n=1..100); # _Robert Israel_, Nov 24 2014
%t Table[Function[p, q = 3; While[! Divisible[q^(p - 1) - 1, p^2], q = NextPrime@ q]; q]@ Prime@ n, {n, 54}] (* _Michael De Vlieger_, Feb 12 2017 *)
%o (PARI) a(n) = {p = prime(n); forprime(q=3, , if (Mod(q, p^2)^(p-1) == 1, return (q)););} \\ _Michel Marcus_, Nov 24 2014
%Y Cf. A125637 (analogous with p^3 instead of p^2).
%Y Cf. A125609 (q=3), A125610 (q=5), A125611 (q=7), A125612 (q=11), A125632 (q=13), A125633 (q=17), A125634 (q=19): sequences of smallest prime p such that q^n divides p^(q-1) - 1.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Nov 28 2006
%E Removed an incorrect comment. - _Felix Fröhlich_, Feb 12 2017
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