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

1,6

Comments

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

Links

Table of n, a(n) for n=1..63.

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A226651 A073711 A071690 * A114653 A069481 A098911

Adjacent sequences: A319176 A319177 A319178 * A319180 A319181 A319182

Keyword

nonn

Author

Gus Wiseman, Sep 12 2018

Status

approved