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

0,32

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.

Links

Table of n, a(n) for n=0..78.

Index entries for sequences related to partitions

Index entries for sequences related to Egyptian fractions

Example

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.

Crossrefs

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

Sequence in context: A143535 A301366 A250100 * A016270 A219493 A284092

Adjacent sequences: A339624 A339625 A339626 * A339628 A339629 A339630

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 10 2020

Status

approved