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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
OFFSET
1,4
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 12 2018
STATUS
approved