A243017 Least number k > 0 such that k*n/(k+n) and k*n/(k-n) are integers or 0 if no such k exists.

0, 0, 6, 12, 0, 3, 0, 24, 18, 15, 0, 4, 0, 0, 10, 48, 0, 9, 0, 30, 28, 0, 0, 8, 0, 0, 54, 21, 0, 15, 0, 96, 66, 0, 210, 12, 0, 0, 78, 24, 0, 21, 0, 132, 30, 0, 0, 16, 0, 75, 102, 156, 0, 27, 66, 42, 114, 0, 0, 12, 0, 0, 84, 192, 0, 33, 0, 204, 138, 105, 0, 24, 0, 0, 50, 228

Offset: 1

Author

Derek Orr, May 29 2014

Keywords

• nonn
• look

Examples

			3*6/(6+3) = 2 and 3*6/(6-3) = 9 are both integers. Thus a(3) = 6.
		

Links

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

Crossrefs

Cf. A243045, A243046, A243047 (positions of 0's), A360120 (their characteristic function).

Programs

PARI

a(n)=for(k=1,n*(n+1),if(k!=n,if((k*n)%(k+n)==0&&(k*n)%(k-n)==0,return(k))))
n=1;while(n<100,print1(a(n),", ");n+=1)