A318715 Number of strict integer partitions of n with relatively prime parts in which no two parts are relatively prime.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 4, 0, 3, 0, 1, 0, 5, 0, 8, 0, 2, 0, 5, 0, 10, 0, 4, 0, 13, 0, 15, 0, 3, 1, 13, 0, 19, 0, 9, 1, 24, 0, 20

Offset

1,41

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..500

Example

The a(67) = 10 strict integer partitions are
  (45,12,10) (42,15,10) (40,15,12) (33,22,12) (28,21,18)
  (36,15,10,6) (30,15,12,10) (28,21,12,6) (24,18,15,10)
  (24,15,12,10,6).

Mathematica

Table[Length[Select[IntegerPartitions[n], And[UnsameQ@@#, GCD@@#==1, And@@(GCD[##]>1&)@@@Select[Tuples[#, 2], Less@@#&]]&]], {n, 50}]

Crossrefs

Cf. A007359, A051185, A078374, A303140, A303282, A303283, A305713, A305843, A305854, A318716, A318717, A318720.

Sequence in context: A290542 A359300 A029834 * A202385 A029833 A050948

Adjacent sequences: A318712 A318713 A318714 * A318716 A318717 A318718

Keyword

nonn

Author

Gus Wiseman, Sep 02 2018

Extensions

a(71)-a(85) from Robert Price, Sep 08 2018

Status

approved