A318584 Number of integer partitions of n whose sum of reciprocals squared is 1.

0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 1, 1, 2, 3, 0, 1, 1, 6, 2, 3, 2, 6, 2, 2, 3, 2, 6, 7, 2, 4, 3, 9, 4, 7, 5, 8, 8, 7, 9, 9, 11, 12, 7, 9, 11, 17, 9, 13, 12, 17, 16, 13, 15, 20, 26, 27, 18, 23

Offset: 0

Author

Gus Wiseman, Aug 29 2018

Keywords

• nonn

Comments

The a(16) = 1 integer partition:

(6,3,3,2,2,2)

The a(48) = 2 integer partitions:

(18,9,9,3,3,2,2,2)

(6,6,6,6,3,3,3,3,3,3,3,3)

The a(56) = 3 integer partitions:

(12,6,6,4,4,4,4,4,4,4,2,2)

(10,6,5,5,5,5,5,5,3,3,2,2)

(6,6,4,4,4,4,4,4,4,4,3,3,3,3)

The a(60) = 6 integer partitions:

(12,12,12,12,3,3,2,2,2)

(8,8,8,8,6,4,4,4,3,3,2,2)

(6,6,6,6,6,6,6,6,6,2,2,2)

(12,12,12,4,3,3,3,3,3,3,2)

(10,5,5,5,5,5,5,4,4,4,4,2,2)

(6,4,4,4,4,4,4,4,4,4,4,4,4,3,3)

Crossrefs

Cf. A000041, A051908, A058360, A289506, A289507, A316854, A316855.

Cf. A318585, A318586, A318587, A318588, A318589.

Programs

Mathematica

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

Extensions

a(61)-a(100) from Alois P. Heinz, Aug 30 2018