A059592 - OEIS

%I #19 Nov 12 2023 13:04:57

%S 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,

%T 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,

%U 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

%N Square-full part of n^2 + 1.

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

%C A124808 gives number of numbers m <= n with a(m)=1. - _Reinhard Zumkeller_, Nov 08

%H Reinhard Zumkeller, <a href="/A059592/b059592.txt">Table of n, a(n) for n = 0..1000</a> (corrected by _Sean A. Irvine_)

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

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

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

%o (PARI) a(n) = core(n^2+1, 1)[2]; \\ _Michel Marcus_, Nov 12 2023

%Y Cf. A000188, A059591, A007913, A002522.

%K easy,nonn

%O 0,8

%A _Marc LeBrun_, Jan 25 2001