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Number of pairs (x,y) 1<=x<=y<=n such that 1/x+1/y+1/n = 1/2.
0

%I #5 Mar 30 2012 18:39:11

%S 0,0,0,0,0,1,0,1,0,1,0,2,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Number of pairs (x,y) 1<=x<=y<=n such that 1/x+1/y+1/n = 1/2.

%F It seems that for n>=43 a(n) = 0

%o (PARI) a(n)=sum(i=1,n,sum(j=1,i,if(1/i+1/j+1/n-1/2,0,1)))

%K nonn

%O 1,12

%A _Benoit Cloitre_, Dec 08 2002