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%I #16 May 15 2022 23:48:56
%S 1,7,239,268,307,18543,2943,485298,330182,478707,24208144,22709274,
%T 2189376182,284862638,599832943,19696179,314198789,3558066693,
%U 69971515635443,18986886768,18710140581,104279454193
%N Largest number k such that the greatest prime factor of k^2+1 is A002313(n), the n-th prime not congruent to 3 mod 4.
%C For any prime p, there are finitely many k such that k^2+1 has p as its largest prime factor.
%C Numbers k such that k^2+1 is p-smooth appear in arctan-relations for the computation of Pi (for example, Machin's identity Pi/4 = 4*arctan(1/5) - arctan(1/239)), see the fxtbook link. [_Joerg Arndt_, Jul 02 2012]
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 32.5 "Arctangent relations for Pi", pp. 633-640.
%H Filip Najman, <a href="http://web.math.hr/~fnajman/smooth.pdf">Smooth values of some quadratic polynomials</a>, Glasnik Matematicki Series III 45 (2010), pp. 347-355.
%H Florian Luca, <a href="http://www.emis.de/journals/AMI/2004/acta2004-luca.pdf">Primitive divisors of Lucas sequences and prime factors of x^2 + 1 and x^4 + 1</a>, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae 31 (2004), pp. 19-24.
%H Filip Najman, <a href="http://web.math.hr/~fnajman/">Home Page</a> (gives all 811 numbers x such that x^2+1 has no prime factor greater than 197)
%Y Equivalents for other polynomials: A175607 (k^2 - 1), A145606 (k^2 + k).
%K nonn,hard,more
%O 1,2
%A _Charles R Greathouse IV_, Feb 21 2011
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