A066761 Number of positive integers of the form (n^2+k^2)/(n-k) for k=1,2,3,4,....,n-1.

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, 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, 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

Offset: 2

Author

Benoit Cloitre, Jan 17 2002

Keywords

• nonn

Comments

Also the number of factors of 2*n^2 which are less than n. - Vladeta Jovovic, Dec 12 2002

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

Examples

			a(2)=1 because (2^2+1)/(2-1) is the only integer of this form.
		

Formula

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)).

Extensions

Corrected by Vladeta Jovovic, Dec 12 2002