A316897 Number of integer partitions of n into relatively prime parts whose reciprocal sum is 1.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 3, 1, 2, 1, 1, 1, 2, 1, 5, 3, 1, 1, 5, 2, 9, 3, 3, 3, 4, 2, 6, 6, 3, 4, 9, 5, 10, 5, 10, 9, 15, 10, 21, 12, 14, 16, 18, 9, 30, 18, 17, 17, 28, 16, 29, 26, 26, 30, 28, 33, 48, 31

Offset

1,22

Comments

The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.

Links

Table of n, a(n) for n=1..80.

Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums

Example

The a(43) = 9 partitions:
(24,8,4,4,3)
(21,7,7,6,2)
(20,12,5,3,3)
(20,8,8,5,2)
(15,15,6,5,2)
(15,12,10,4,2)
(14,7,7,7,4,4)
(12,8,8,6,6,3)
(10,10,10,5,4,4).

Mathematica

Table[Length[Select[IntegerPartitions[n], And[GCD@@#==1, Sum[1/m, {m, #}]==1]&]], {n, 30}]

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316888-A316904.

Sequence in context: A309395 A260943 A316893 * A151756 A112053 A089798

Adjacent sequences: A316894 A316895 A316896 * A316898 A316899 A316900

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Extensions

a(71)-a(80) from Giovanni Resta, Jul 16 2018

Status

approved