A243047 Numbers n such that k*n/(k-n) and k*n/(k+n) are both never integers for k > 0.

1, 2, 5, 7, 11, 13, 14, 17, 19, 22, 23, 25, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 49, 53, 58, 59, 61, 62, 65, 67, 71, 73, 74, 77, 79, 82, 83, 85, 86, 89, 94, 95, 97, 98, 101, 103, 106, 107, 109, 113, 115, 118, 119, 121, 122, 125, 127, 131, 133, 134, 137, 139, 142, 145, 146

Offset: 1

Author

Derek Orr, May 29 2014

Keywords

• nonn

Comments

a(n) is numbers n such that A243017(n) = A243045(n) = A243046(n) = 0.

Examples

			Consider 2*k/(k-2) and 2*k/(k+2). The largest k that would make these integers is 2*(2+1) and 2*(2-1), respectively. So if k = 1, 2, 3, 4, 5, or 6, the expressions become {-2,2/3}, {undef,1}, {6,6/5}, {4,8/6}, {10/3,10/7}, {4,12/8}. In any of these sets, both are not integers and thus, for any k > 0, both will never be integers. So 2 is a member of this sequence.
		

Crossrefs

Cf. A243017, A243045, A243046.

Programs

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)}
n=1,while(n<200,if(a(n)==0,print1(a(n),", "));n+=1)