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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 24 11:19 EDT 2019. Contains 323529 sequences. (Running on oeis4.)