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For n != 1 mod 3, we can write 3/(2n+1) = 1/a + 1/b + 1/c with a>b>c>0, a,b,c distinct and odd; sequence gives smallest such a, or 1 if n = 1 mod 3.
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%I #7 Mar 31 2012 12:34:58

%S 1,15,35,1,165,91,1,153,247,1,207,75,1,435,651,1,63,185,1,615,1247,1,

%T 2961,245,1,371,99,1,1239,1891,1,105,3015,1,1917,2701,1,99,4187,1,

%U 9213,187,1,4005,143,1,285,3395,1,1313,4017,1,15301,5995,1,4407,345

%N For n != 1 mod 3, we can write 3/(2n+1) = 1/a + 1/b + 1/c with a>b>c>0, a,b,c distinct and odd; sequence gives smallest such a, or 1 if n = 1 mod 3.

%e 1/15+1/5+1/3=3/5; 1/35+1/15+1/3=3/7; 1/165+1/15+1/5=3/11; 1/91+1/13+1/7=3/13

%Y Cf. A027442.

%K nonn

%O 1,2

%A _N. J. A. Sloane_ and _R. H. Hardin_