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

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

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 *)

Prog

(PARI) a(n) = {my(f = factor(prod(x=1, n, x^2+1))); f[length(f~), 1]}
(Magma) a := AssociativeArray(); a[1] := 2; for n in [2..55] do f := Factorisation(n^2 + 1);
    maxFactor := Maximum([x[1] : x in f]); a[n] := Max(a[n-1], maxFactor); end for;
seq := [a[n] : n in [1..55]]; seq; // Vincenzo Librandi, Jan 13 2026

Crossrefs

Cf. A002496, A002522, A005574, A014442.

Sequence in context: A281793 A259036 A081235 * A082534 A165659 A154816

Adjacent sequences: A219583 A219584 A219585 * A219587 A219588 A219589

Keyword

nonn

Author

Michel Marcus, Nov 23 2012

Status

approved