A318717 Number of strict integer partitions of n in which no two parts are relatively prime.

1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 5, 1, 5, 4, 6, 1, 10, 1, 11, 6, 12, 1, 19, 3, 18, 8, 23, 1, 36, 2, 32, 13, 38, 7, 57, 2, 54, 19, 68, 3, 95, 3, 90, 33, 104, 3, 148, 7, 149, 40, 166, 5, 230, 17, 226, 56, 256, 6, 360, 9, 340, 84, 390, 25, 527, 11, 513, 109

Offset

0,7

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600

Example

The a(20) = 11 partitions:
  (20),
  (12,8), (14,6), (15,5), (16,4), (18,2),
  (10,6,4), (10,8,2), (12,6,2), (14,4,2),
  (8,6,4,2).

Mathematica

Table[Length[Select[IntegerPartitions[n], And[UnsameQ@@#, And@@(GCD[##]>1&)@@@Select[Tuples[#, 2], Less@@#&]]&]], {n, 30}]

Crossrefs

Cf. A000009, A007359, A007360, A051185, A302569, A302797, A303140, A303280, A303283, A305713, A305843, A305854, A305713, A318715, A318719.

Sequence in context: A070104 A131085 A303280 * A331887 A328220 A134192

Adjacent sequences: A318714 A318715 A318716 * A318718 A318719 A318720

Keyword

nonn

Author

Gus Wiseman, Sep 02 2018

Extensions

a(51)-a(69) from Alois P. Heinz, Sep 02 2018

Status

approved