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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
OFFSET
1,6
COMMENTS
An integer partition is aperiodic if its multiplicities are relatively prime.
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 12 2018
STATUS
approved