A316891 Number of aperiodic integer partitions of n into relatively prime parts whose reciprocal sum is an integer.

1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 5, 2, 7, 4, 7, 6, 13, 7, 18, 12, 20, 17, 32, 20, 39, 31, 47, 45, 74, 56, 96, 83, 109, 105, 151, 130, 199, 183, 234, 232, 319, 286, 404, 386, 473, 488, 638, 599, 782, 767, 931, 960, 1197, 1165, 1465, 1477, 1747, 1814, 2212, 2196

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(17) = 13 partitions:
(6443),
(44441),
(3332222), (6322211),
(44222111),
(222222221), (333221111), (632111111),
(4421111111),
(22222211111), (33311111111),
(2222111111111),
(221111111111111).

Mathematica

Table[Length[Select[IntegerPartitions[n], And[GCD@@#==1, GCD@@Length/@Split[#]==1, IntegerQ[Sum[1/m, {m, #}]]]&]], {n, 50}]

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316856, A316888-A316904.

Sequence in context: A262213 A178913 A142721 * A152992 A185727 A070951

Adjacent sequences: A316888 A316889 A316890 * A316892 A316893 A316894

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Extensions

a(51)-a(60) from Alois P. Heinz, Jul 18 2018

Status

approved