A316896 Number of aperiodic integer partitions of n whose reciprocal sum is 1.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 3, 5, 5, 2, 2, 5, 5, 9, 3, 4, 6, 4, 3, 6, 8, 4, 10, 9, 8, 11, 7, 13, 12, 15, 15, 21, 18, 16, 21, 19, 17, 30, 23, 19, 23, 28, 25, 29, 34, 29, 44, 28, 46, 48, 42

Offset

1,22

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..80.

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

Example

The a(37) = 5 partitions are (24,8,3,2), (20,5,4,4,4), (15,10,6,3,3), (14,7,7,7,2), (10,10,10,5,2).

Mathematica

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

Crossrefs

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

Sequence in context: A046094 A055976 A293305 * A230626 A363946 A354824

Adjacent sequences: A316893 A316894 A316895 * A316897 A316898 A316899

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Extensions

a(51)-a(80) from Giovanni Resta, Jul 16 2018

Status

approved