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

Author

Gus Wiseman, Sep 12 2018

Keywords

• nonn

Examples

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

Crossrefs

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

Programs

Mathematica

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