A059591 Squarefree part of n^2+1.

1, 2, 5, 10, 17, 26, 37, 2, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 13, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 41, 1090, 1157, 1226, 1297, 1370, 5, 1522, 1601, 2, 1765, 74, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602

Offset: 0

Author

Marc LeBrun, Jan 25 2001

Keywords

• easy
• nonn

Comments

Related to period-1 continued fractions [z,z,z,...].

Examples

			a(7)=2 since 7^2+1 = 50 = 25*2 = (5^2)*2.
		

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A007913, A059592, A000188.

Programs

Maple

A:= proc(n)
local F;
F:= select(t -> t[2]::odd, ifactors(n^2+1)[2]);
mul(t[1],t=F)
end proc:
map(A, [$0..100]); # Robert Israel, Jun 18 2015

Mathematica

Table[Times @@ Flatten[Table[#1, {#2}] & @@@ Select[FactorInteger[n^2 + 1], OddQ@ Last@ # &]], {n, 120}] (* Michael De Vlieger, Jun 19 2015 *)

PARI

a(n) = core(n^2+1); \\ Michel Marcus, Jun 18 2015

Formula

a(n) = A007913(n^2+1).

a(n)*A059592(n)^2 = n^2+1.