A243046 Number of solutions to k*n/(k+n) = x and k*n/(k-n) = y for integers x and y and natural number k.

0, 0, 1, 1, 0, 2, 0, 1, 1, 1, 0, 5, 0, 0, 3, 1, 0, 2, 0, 2, 2, 0, 0, 7, 0, 0, 1, 2, 0, 5, 0, 1, 1, 0, 1, 6, 0, 0, 1, 4, 0, 4, 0, 1, 4, 0, 0, 7, 0, 1, 1, 1, 0, 2, 1, 2, 1, 0, 0, 13, 0, 0, 3, 1, 0, 3, 0, 1, 1, 2, 0, 8, 0, 0, 3, 1, 0, 3, 0, 4, 1, 0, 0, 10, 0, 0, 1, 1, 0, 7, 1, 1, 1, 0, 0, 7, 0, 0, 2

Offset: 1

Author

Derek Orr, May 29 2014

Keywords

• nonn

Comments

Question: Is there any direct formula for this sequence? Cf. for example A146564. - Antti Karttunen, Feb 18 2023

Examples

			6*k/(k-6) and 6*k/(k+6) are integers for k = 3 (-6 and 2, respectively) and k = 12 (12 and 4, respectively). Thus a(6) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080

Crossrefs

Cf. A063647, A146564, A243017, A243045, A243047 (positions of 0's), A360120 (their characteristic function).

Programs

PARI

A243046(n) = sum(k=1, n*(n+1), (k!=n && !((k*n)%(k+n)) && !((k*n)%(k-n)))); \\ [improved by Antti Karttunen, Feb 18 2023]

Formula

a(n) <= A063647(n), a(n) <= A146564(n). - Antti Karttunen, Feb 18 2023