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

0,42

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)

Links

Table of n, a(n) for n=0..100.

Mathematica

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

Crossrefs

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

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

Sequence in context: A374355 A279479 A343630 * A177338 A024158 A054978

Adjacent sequences: A318581 A318582 A318583 * A318585 A318586 A318587

Keyword

nonn

Author

Gus Wiseman, Aug 29 2018

Extensions

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

Status

approved