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

2, 5, 5, 17, 17, 37, 37, 37, 41, 101, 101, 101, 101, 197, 197, 257, 257, 257, 257, 401, 401, 401, 401, 577, 577, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 1297, 1297, 1297, 1297, 1601, 1601, 1601, 1601, 1601, 1601, 1601, 1601, 1601, 1601, 1601, 1601

Offset: 1

Author

Michel Marcus, Nov 23 2012

Keywords

• nonn

Links

• C. Hooley, On the greatest prime factor of a quadratic polynomial, Acta Mathematica July 1967, Volume 117, Issue 1, pp 281-299.

Crossrefs

Cf. A002496, A002522, A005574, A014442.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      max(a(n-1), numtheory[factorset](n^2+1)[]))
    end:
seq(a(n), n=1..55);  # Alois P. Heinz, Jan 03 2021

Mathematica

a[n_] := a[n] = If[n == 1, 2, Max[a[n-1], FactorInteger[n^2+1][[-1, 1]]]];
Table[a[n], {n, 1, 55}] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)

PARI

a(m) = {for (n=1, m, f = factor(prod(x=1, n, x^2+1)); print1(f[length(f~), 1], ", "););}