This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A066761 #10 Jul 09 2015 22:04:21 %S A066761 1,2,2,2,4,2,3,4,5,2,7,2,5,7,4,2,8,2,7,8,5,2,10,4,5,6,7,2,15,2,5,8,5, %T A066761 7,13,2,5,8,10,2,15,2,8,12,5,2,13,4,9,8,8,2,12,8,10,8,5,2,23,2,5,13,6, %U A066761 8,15,2,8,8,16,2,17,2,5,13,8,7,16,2,13,8,5,2,23,8,5,8,10,2,26,7,8,8,5,8 %N A066761 Number of positive integers of the form (n^2+k^2)/(n-k) for k=1,2,3,4,....,n-1. %C A066761 Also the number of factors of 2*n^2 which are less than n. - _Vladeta Jovovic_, Dec 12 2002 %C A066761 Also the number of factors of 2*n^2 which are greater than 2*n, so a(n) = tau(2*n^2)-1-A055081(n). - _Vladeta Jovovic_, Dec 13 2002 %F A066761 No general formula is known but let k be a positive integer, p and q distinct odd primes then a(2^k)=k a(p^k)=2*k a(p*q)= 7 or 8 if p >13 a(2*p)= 5 if p>5 a(9*p^2)= 23 .... Asymptotic formula: (1/n)*sum(i=1, n, a(i))= log(n)*log(log(n))+o(log(n)). %e A066761 a(2)=1 because (2^2+1)/(2-1) is the only integer of this form. %K A066761 nonn %O A066761 2,2 %A A066761 _Benoit Cloitre_, Jan 17 2002 %E A066761 Corrected by _Vladeta Jovovic_, Dec 12 2002