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 A243064 Numbers n such that k*n/(k+n) and k*n/(k-n) are integers for only one k > 0. 0

%I

%S 3,4,8,9,10,16,27,32,33,35,39,44,50,51,52,55,57,64,68,69,76,81,87,88,

%T 91,92,93,104,111,116,117,123,124,128,129,130,141,143,148,152,154,159,

%U 164,170,172,175,176,177,182,183,184,188,201,207,208,212,213,219,230,232,236,237

%N Numbers n such that k*n/(k+n) and k*n/(k-n) are integers for only one k > 0.

%C a(n) = numbers n such that A243046(n) = 1.

%e 4*k/(4+k) and 4*k/(4-k) can both be integers only when k <= 4*3 = 12. Plugging in k = 1, 2, 3, ... 12, one can see that only k = 12 works for both of these expressions (3 and -6, respectively). So 4 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<300,if(a(n)==1,print1(n,", "));n+=1)

%Y Cf. A243046.

%K nonn

%O 1,1

%A _Derek Orr_, May 30 2014

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Last modified January 26 11:13 EST 2020. Contains 331279 sequences. (Running on oeis4.)