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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 12 2018
STATUS
approved