A319162 Number of periodic integer partitions of n whose multiplicities are aperiodic, meaning the multiplicities of these multiplicities are relatively prime.

0, 1, 1, 2, 1, 3, 1, 4, 2, 6, 1, 9, 1, 12, 6, 16, 1, 27, 1, 33, 12, 46, 1, 70, 5, 84, 22, 110, 1, 172, 1, 188, 46, 251, 15, 366, 1, 418, 84, 540, 1, 775, 1, 863, 162, 1095, 1, 1535, 11, 1750, 251, 2154, 1, 2963, 49, 3323, 418, 4106, 1, 5567

Offset

1,4

Links

Table of n, a(n) for n=1..60.

Example

The a(12) = 9 partitions:
  (66),
  (444), (441111),
  (3333), (33111111),
  (222222), (222111111), (2211111111),
  (111111111111).

Mathematica

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

Crossrefs

Cf. A000837, A018783, A047966, A098859, A100953, A305563, A319149, A319160, A319163, A319164.

Sequence in context: A113322 A007380 A369813 * A029171 A354185 A322994

Adjacent sequences: A319159 A319160 A319161 * A319163 A319164 A319165

Keyword

nonn

Author

Gus Wiseman, Sep 12 2018

Status

approved