A318586 Number of integer partitions of n whose sum of reciprocals squared is the reciprocal of an integer.

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 3, 1, 2, 3, 3, 1, 4, 1, 3, 1, 2, 1, 5, 2, 1, 4, 5, 1, 5, 1, 6, 3, 2, 4, 8, 2, 4, 2, 6, 3, 9, 2, 4, 7, 5, 4, 11, 8, 7, 8, 9, 5, 12, 5, 16, 5, 10, 5, 25, 10, 9, 13, 18, 12, 18, 6, 11, 14, 22, 9, 24, 11, 21, 22, 25, 24, 23, 28, 32

Offset

1,4

Links

Giovanni Resta, Table of n, a(n) for n = 1..150

Example

The a(42) = 9 integer partitions:
  (42)
  (21,14,7)
  (18,9,9,6)
  (18,9,9,3,3)
  (20,10,4,4,4)
  (12,12,12,4,2)
  (10,5,5,5,5,5,5,2)
  (12,6,6,4,4,4,2,2,2)
  (6,6,4,4,4,4,3,3,3,3,2)

Mathematica

Table[Length[Select[IntegerPartitions[n], IntegerQ[1/Total[#^(-2)]]&]], {n, 30}]

Crossrefs

Cf. A000041, A051908, A058360, A289506, A289507, A316854, A316857.

Cf. A318584, A318585, A318587, A318588, A318589.

Sequence in context: A336424 A353236 A325939 * A222580 A376140 A316978

Adjacent sequences: A318583 A318584 A318585 * A318587 A318588 A318589

Keyword

nonn

Author

Gus Wiseman, Aug 29 2018

Extensions

a(61)-a(80) from Giovanni Resta, Sep 03 2018

Status

approved