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A051907 Number of ways to express 1 as the sum of distinct unit fractions such that the sum of the denominators is n. 4

%I

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

%T 0,0,1,1,0,0,0,0,1,0,2,0,0,0,0,2,0,1,1,1,1,0,2,0,1,1,1,2,0,4,1,3,4,0,

%U 2,0,6,0,1,2,1,3,0,4,2,1,5,5,3,2,3,3,5,5,5,2,1,12,5,4,11,4,5,2,11,3,5

%N Number of ways to express 1 as the sum of distinct unit fractions such that the sum of the denominators is n.

%H Seiichi Manyama, <a href="/A051907/b051907.txt">Table of n, a(n) for n = 1..150</a>

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%e 1 = 1/2+1/4+1/9+1/12+1/18 = 1/2+1/5+1/6+1/12+1/20. The sum of the denominators of each of these is 45, these are the only 2 with sum of denominators = 45, so a(45)=2.

%Y A051882 lists n such that a(n)=0.

%Y Cf. A051908.

%K nonn

%O 1,45

%A _Jud McCranie_, Dec 16 1999

%E R. L. Graham showed that a(n)>0 for n>77.

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Last modified September 25 23:09 EDT 2021. Contains 347664 sequences. (Running on oeis4.)