A339627 Number of partitions of n into distinct parts such that the sum of reciprocals of parts is an integer.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 3, 2, 4, 5, 4, 7, 4, 2, 2, 6, 6, 1, 3, 3, 4, 3, 4

Offset: 0

Author

Ilya Gutkovskiy, Dec 10 2020

Keywords

• nonn

Comments

Also the number of ways to express an integer as the sum of distinct unit fractions such that the sum of the denominators is n.

Examples

			a(31) = 2 because we have 2 + 4 + 5 + 20 = 1 + 2 + 3 + 10 + 15 = 31 and 1/2 + 1/4 + 1/5 + 1/20 = 1, 1/1 + 1/2 + 1/3 + 1/10 + 1/15 = 2 are integers.
		

Links

• Index entries for sequences related to partitions
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A051907, A051908, A058360, A339628, A339629.