A319179 Number of integer partitions of n that are relatively prime but not aperiodic. Number of integer partitions of n that are aperiodic but not relatively prime.

0, 1, 1, 1, 1, 2, 1, 3, 2, 6, 1, 9, 1, 14, 7, 17, 1, 32, 1, 36, 15, 55, 1, 77, 6, 100, 27, 121, 1, 200, 1, 209, 56, 296, 19, 403, 1, 489, 101, 596, 1, 885, 1, 947, 192, 1254, 1, 1673, 14, 1979, 297, 2336, 1, 3300, 60, 3594, 490, 4564, 1, 5988, 1, 6841, 800

Offset: 1

Author

Gus Wiseman, Sep 12 2018

Keywords

• nonn

Comments

An integer partition is aperiodic if its multiplicities are relatively prime.

Examples

			The a(12) = 9 integer partitions that are relatively prime but not aperiodic:
  (5511),
  (332211), (333111), (441111),
  (22221111), (33111111),
  (222111111),
  (2211111111),
  (111111111111).
The a(12) = 9 integer partitions that are aperiodic but not relatively prime:
  (12),
  (8,4), (9,3), (10,2),
  (6,3,3), (6,4,2), (8,2,2),
  (6,2,2,2),
  (4,2,2,2,2).
		

Crossrefs

Cf. A000837, A018783, A047966, A100953, A305563, A319149, A319160, A319162, A319164.

Programs

Mathematica

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