A252096 Largest prime divisor of n^2+1 - smallest prime divisor of n^2+1.

0, 0, 3, 0, 11, 0, 3, 8, 39, 0, 59, 24, 15, 0, 111, 0, 27, 8, 179, 0, 15, 92, 51, 0, 311, 0, 71, 152, 419, 36, 35, 36, 107, 76, 611, 0, 135, 12, 759, 0, 27, 348, 35, 136, 1011, 44, 15, 456, 1199, 20, 1299, 536, 279, 0, 87, 0, 11, 668, 1739, 264, 1859, 764, 395

Offset: 1

Author

Michel Lagneau, Dec 14 2014

Keywords

• nonn
• easy

Examples

			a(5)= 11 because 5^2+1 = 2*13 and 13-2 = 11.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002522 (n^2+1), A005574 (n^2+1 is prime).

Cf. A014442 (largest prime factor of n2+1), A089120 (smallest prime factor).

Programs

Maple

with(numtheory):
a:= n-> (f-> max(f[])-min(f[]))(factorset(n^2+1)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 07 2015

Mathematica

f[n_]:=Transpose[FactorInteger[n^2+1]][[1]]; Table[Last[f[n]-First[f[n]]], {n, 200}]

PARI

a(n) = {my(f = factor(n^2+1)); f[#f~,1] - f[1,1];} \\ Michel Marcus, Dec 15 2014

Formula

a(n) = A014442(n) - A089120(n).

a(A005574(n)) = 0. - Michel Marcus, Dec 15 2014