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A219586 Greatest prime factor of Product_{x=1..n} (x^2 + 1).

%I A219586 #17 May 14 2022 11:20:43
%S A219586 2,5,5,17,17,37,37,37,41,101,101,101,101,197,197,257,257,257,257,401,
%T A219586 401,401,401,577,577,677,677,677,677,677,677,677,677,677,677,1297,
%U A219586 1297,1297,1297,1601,1601,1601,1601,1601,1601,1601,1601,1601,1601,1601,1601
%N A219586 Greatest prime factor of Product_{x=1..n} (x^2 + 1).
%H A219586 C. Hooley, <a href="http://link.springer.com/content/pdf/10.1007%2FBF02395047">On the greatest prime factor of a quadratic polynomial</a>, Acta Mathematica July 1967, Volume 117, Issue 1, pp 281-299.
%p A219586 a:= proc(n) option remember; `if`(n=0, 0,
%p A219586       max(a(n-1), numtheory[factorset](n^2+1)[]))
%p A219586     end:
%p A219586 seq(a(n), n=1..55);  # _Alois P. Heinz_, Jan 03 2021
%t A219586 a[n_] := a[n] = If[n == 1, 2, Max[a[n-1], FactorInteger[n^2+1][[-1, 1]]]];
%t A219586 Table[a[n], {n, 1, 55}] (* _Jean-François Alcover_, May 14 2022, after _Alois P. Heinz_ *)
%o A219586 (PARI) a(m) = {for (n=1, m, f = factor(prod(x=1, n, x^2+1)); print1(f[length(f~), 1], ", "););}
%Y A219586 Cf. A002496, A002522, A005574, A014442.
%K A219586 nonn
%O A219586 1,1
%A A219586 _Michel Marcus_, Nov 23 2012