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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. 5

%I #9 Feb 18 2023 08:09:16

%S 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,

%T 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,

%U 66,42,114,0,0,12,0,0,84,192,0,33,0,204,138,105,0,24,0,0,50,228

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

%H Antti Karttunen, <a href="/A243017/b243017.txt">Table of n, a(n) for n = 1..10080</a>

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

%o (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))))

%o n=1;while(n<100,print1(a(n),", ");n+=1)

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

%K nonn,look

%O 1,3

%A _Derek Orr_, May 29 2014

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