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Number of integers of the form k^2 + 1 whose greatest prime factor is A002313(n), the n-th prime not congruent to 3 mod 4.
3

%I #10 Jan 03 2025 14:56:00

%S 1,3,5,6,7,10,9,16,17,20,26,36,36,40,46,47,56,67,73,86,97,107

%N Number of integers of the form k^2 + 1 whose greatest prime factor is A002313(n), the n-th prime not congruent to 3 mod 4.

%C See A223702 for additional information.

%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/smooth.pdf">Smooth values of some quadratic polynomials</a>, Glasnik Matematicki Series III 45 (2010), pp. 347-355.

%Y Row lengths of A223702.

%Y First differences of A285283.

%Y Cf. A002313, A177979, A185389.

%K nonn,more

%O 1,2

%A _Andrew Howroyd_, Dec 22 2024