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A316348 a(n) is the smallest k > 1 such that gcd(k, m^k - m) = 1 for all m = 2,...,n.

%I A316348 #50 Dec 16 2022 11:55:11
%S A316348 35,35,77,77,143,143,143,143,299,299,323,323,323,323,437,437,667,667,
%T A316348 667,667,899,899,899,899,899,899,1457,1457,1739,1739,1739,1739,1739,
%U A316348 1739,1763,1763,1763,1763,2021,2021,2491,2491,2491,2491,3127,3127,3127,3127,3127
%N A316348 a(n) is the smallest k > 1 such that gcd(k, m^k - m) = 1 for all m = 2,...,n.
%C A316348 Conjecture: all the terms are in A121707.
%C A316348 From _David A. Corneth_, Aug 13 2018: (Start)
%C A316348 GCD(n, a(n)) = 1. a(n) is odd.
%C A316348 Is a(n) squarefree?
%C A316348 a(n+1) >= a(n) by definition. (End)
%C A316348 It seems that a(prime(n+1)-1) > a(prime(n)-1) for n > 1. - _Thomas Ordowski_, Aug 13 2018
%H A316348 Michel Marcus, <a href="/A316348/b316348.txt">Table of n, a(n) for n = 2..306</a>
%F A316348 Conjecture: a(n) ~ n^2.
%o A316348 (PARI) isok(k, n)= {for (m=2, n, if (gcd(k, m^k - m) != 1, return (0));); return(1);}
%o A316348 a(n) = {my(k=2); while (! isok(k, n), k++); k;} \\ _Michel Marcus_, Aug 13 2018
%Y A316348 Cf. A121707, A267999, A316111.
%K A316348 nonn
%O A316348 2,1
%A A316348 _Thomas Ordowski_, Aug 13 2018
%E A316348 More terms from _Michel Marcus_, Aug 13 2018