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

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, 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, 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

Offset: 1

Author

Jud McCranie, Dec 16 1999

Keywords

• nonn

Examples

			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.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..150
• Index entries for sequences related to Egyptian fractions

Crossrefs

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

Cf. A051908.

Extensions

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