A339628 Number of compositions (ordered 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, 6, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 120, 0, 0, 0, 0, 24, 144, 144, 120, 0, 0, 0, 24, 240, 720, 0, 0, 0, 120, 720, 240, 1440, 0, 0, 0, 840, 5760, 720, 5160, 744, 240, 720, 1440, 10080, 720, 5760, 5160, 1560, 5760, 2280, 16560, 6000, 7560

Offset

0,12

Comments

Also the number of ordered 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..67.

Index entries for sequences related to compositions

Index entries for sequences related to Egyptian fractions

Example

a(11) = 6 because we have 2 + 3 + 6 = 2 + 6 + 3 = 3 + 2 + 6 = 3 + 6 + 2 = 6 + 2 + 3 = 6 + 3 + 2 = 11 and 1/2 + 1/3 + 1/6 = 1 is an integer.

Crossrefs

Cf. A051907, A051908, A058360, A339627, A339629.

Sequence in context: A394308 A154420 A255305 * A304271 A293590 A376513

Adjacent sequences: A339625 A339626 A339627 * A339629 A339630 A339631

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 10 2020

Status

approved