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A319162 Number of periodic integer partitions of n whose multiplicities are aperiodic, meaning the multiplicities of these multiplicities are relatively prime. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A059499 A113322 A007380 * A029171 A322994 A256147

Adjacent sequences:  A319159 A319160 A319161 * A319163 A319164 A319165

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 12 2018

STATUS

approved

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Last modified July 27 04:32 EDT 2021. Contains 346305 sequences. (Running on oeis4.)