A316895 Number of aperiodic integer partitions of n whose reciprocal sum is an integer.

1, 0, 0, 0, 1, 0, 1, 0, 2, 2, 5, 2, 7, 5, 7, 6, 13, 8, 18, 13, 20, 19, 32, 21, 39, 35, 49, 48, 74, 60, 96, 86, 110, 111, 151, 135, 199, 192, 235, 239, 319, 299, 404, 394, 477, 506, 638, 609, 782, 788, 934, 978, 1197, 1193, 1466, 1501, 1752, 1851, 2212, 2227

Offset

1,9

Comments

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

A partition is aperiodic if its multiplicities are relatively prime.

Links

Table of n, a(n) for n=1..60.

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

Example

The a(11) = 5 partitions are (632), (4421), (33311), (2222111), (221111111).

Mathematica

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

Crossrefs

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

Sequence in context: A305797 A029648 A126103 * A100030 A029603 A204202

Adjacent sequences: A316892 A316893 A316894 * A316896 A316897 A316898

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Extensions

a(51)-a(60) from Alois P. Heinz, Jul 17 2018

Status

approved