A092666 a(n) = number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k (for any k), with 0 < x_1 <= ... <= x_k = n.

1, 1, 1, 2, 1, 7, 1, 10, 10, 26, 1, 107, 1, 83, 375, 384, 1, 1418, 1, 4781, 7812, 1529, 1, 33665, 9789, 4276, 27787, 168107, 1, 584667, 1, 586340, 1177696, 52334, 5285597, 14746041, 1, 218959, 13092673, 84854683, 1, 279357910, 1, 491060793, 2001103921

Offset: 1

Author

Max Alekseyev, Mar 02 2004

Keywords

• nonn

Examples

			a(4) = 2 since there are two fractions 1=1/2+1/4+1/4 and 1=1/4+1/4+1/4+1/4.
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..390
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A020473, A092667, A092669, A002966, A000058, A259633.

Formula

a(n) = A020473(n) - A020473(n-1).

a(n) = 1 if n is prime.

Extensions

Edited by Max Alekseyev, May 05 2010