A243047 - OEIS

%I #4 May 30 2014 01:02:13

%S 1,2,5,7,11,13,14,17,19,22,23,25,26,29,31,34,37,38,41,43,46,47,49,53,

%T 58,59,61,62,65,67,71,73,74,77,79,82,83,85,86,89,94,95,97,98,101,103,

%U 106,107,109,113,115,118,119,121,122,125,127,131,133,134,137,139,142,145,146

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

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

%e 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.

%o (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)}

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

%Y Cf. A243017, A243045, A243046.

%K nonn

%O 1,2

%A _Derek Orr_, May 29 2014