A059592 Square-full part of n^2 + 1.

1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 17, 1, 1, 29, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 13, 1, 1, 1

Offset: 0

Author

Marc LeBrun, Jan 25 2001

Keywords

• easy
• nonn

Comments

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

A124808 gives number of numbers m <= n with a(m)=1. - Reinhard Zumkeller, Nov 08

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 (corrected by _Sean A. Irvine_)

Crossrefs

Cf. A000188, A059591, A007913, A002522.

Programs

PARI

a(n) = core(n^2+1, 1)[2]; \\ Michel Marcus, Nov 12 2023

Formula

a(n) = A000188(A002522(n)).

a(n)^2 * A059591(n) = n^2 + 1.