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

1,6

Comments

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

Links

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

Formula

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

Example

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.

Prog

(PARI) a(n)={t=0; for(k=1, n*(n+1), if(k!=n, if((k*n)%(k+n)==0&&(k*n)%(k-n)==0, t+=1))); return(t)} \\ - Typo corrected by Antti Karttunen, Feb 18 2023
n=1, while(n<100, print1(a(n), ", "); n+=1)
(PARI) A243046(n) = sum(k=1, n*(n+1), (k!=n && !((k*n)%(k+n)) && !((k*n)%(k-n)))); \\ Antti Karttunen, Feb 18 2023

Crossrefs

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

Sequence in context: A099362 A321378 A307039 * A058940 A141684 A152492

Adjacent sequences: A243043 A243044 A243045 * A243047 A243048 A243049

Keyword

nonn

Author

Derek Orr, May 29 2014

Status

approved