A319164 Number of integer partitions of n that are neither relatively prime nor aperiodic.

0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 5, 0, 2, 2, 5, 0, 6, 0, 9, 2, 2, 0, 17, 1, 2, 3, 17, 0, 18, 0, 22, 2, 2, 2, 48, 0, 2, 2, 48, 0, 34, 0, 58, 11, 2, 0, 111, 1, 14, 2, 103, 0, 65, 2, 141, 2, 2, 0, 264, 0, 2, 19, 231, 2, 116, 0, 299, 2, 42

Offset

1,6

Comments

A partition is aperiodic if its multiplicities are relatively prime.

Links

Table of n, a(n) for n=1..70.

Example

The a(24) = 17 integer partitions:
  (12,12),
  (8,8,8),
  (6,6,6,6), (8,8,4,4), (9,9,3,3), (10,10,2,2),
  (4,4,4,4,4,4), (6,6,3,3,3,3), (6,6,4,4,2,2), (6,6,6,2,2,2), (8,8,2,2,2,2),
  (3,3,3,3,3,3,3,3), (4,4,4,4,2,2,2,2), (6,6,2,2,2,2,2,2),
  (4,4,4,2,2,2,2,2,2),
  (4,4,2,2,2,2,2,2,2,2),
  (2,2,2,2,2,2,2,2,2,2,2,2).

Mathematica

Table[Length[Select[IntegerPartitions[n], And[GCD@@#>1, GCD@@Length/@Split[#]>1]&]], {n, 30}]

Crossrefs

Cf. A000837, A018783, A047966, A098859, A100953, A305563, A319149, A319160, A319162, A319165.

Sequence in context: A174725 A348537 A071459 * A070288 A329643 A352697

Adjacent sequences: A319161 A319162 A319163 * A319165 A319166 A319167

Keyword

nonn

Author

Gus Wiseman, Sep 12 2018

Status

approved