A144063 Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n <= 256.

1, 0, 1, 6, 62, 642, 5623, 47126, 368680, 2715613, 18876751, 124137535, 774232619, 4595291801, 26030660449, 141031079451, 731862267491, 3641135367129, 17379359388167, 79633646141291, 350541406992141, 1483638948734104, 6043258919626951, 23713645892145709

Offset: 1

Author

Zhao Hui Du, Sep 09 2008

Keywords

• nonn
• fini

Comments

Egyptian fraction for a rational number is to represent the number in sum of some distinct unit fraction, such as 1 = 1/2 + 1/3 + 1/6, here we represent 1 by a three terms Egyptian fraction and the largest denominator is 6. And the representation is non-unique.

There are a total of 3007198863516917545589795267613 Egyptian fractions for 1 whose largest denominator is no more than 256.

Examples

			a(1)=1 since 1 = 1/1.
a(2)=0 since the sum of any two distinct unit fractions are not 1.
a(3)=1 since the only three terms Egyptian fraction for 1 is 1/2 + 1/3 + 1/6.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..114
• Eric Weisstein's World of Mathematics, Egyptian Fraction
• link for the result [Broken link]

Crossrefs

Cf. A002967, A006585.

Formula

a(n) = 0 for n > 114.