A243045 Largest number k such that k*n/(k+n) and k*n/(k-n) are integers or 0 if no such number exists.

0, 0, 6, 12, 0, 12, 0, 24, 18, 15, 0, 60, 0, 0, 60, 48, 0, 36, 0, 60, 42, 0, 0, 168, 0, 0, 54, 84, 0, 120, 0, 96, 66, 0, 210, 180, 0, 0, 78, 360, 0, 105, 0, 132, 180, 0, 0, 336, 0, 75, 102, 156, 0, 108, 66, 168, 114, 0, 0, 660, 0, 0, 504, 192, 0, 132, 0, 204, 138, 420, 0, 504

Offset: 1

Author

Derek Orr, May 29 2014

Keywords

• nonn
• look

Examples

			k*3/(k-3) and k*3/(k+3) are integers only for k=6. Thus since 6 is the largest k-value, a(3) = 6.
		

Links

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

Crossrefs

Cf. A243017, A243046, A243047 (positions of 0's), A360120 (their characteristic function).

Programs

PARI

a(n)=for(k=-n*(n+1),0,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)