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A356067
Number of integer partitions of n into relatively prime prime-powers.
1
0, 0, 0, 0, 0, 1, 0, 3, 2, 5, 4, 11, 7, 18, 16, 26, 27, 43, 41, 65, 65, 92, 100, 137, 142, 194, 210, 270, 295, 379, 410, 519, 571, 699, 782, 947, 1046, 1267, 1414, 1673, 1870, 2213, 2465, 2897, 3230, 3757, 4210, 4871, 5427, 6265, 6997
OFFSET
0,8
EXAMPLE
The a(5) = 1 through a(12) = 7 partitions:
(32) . (43) (53) (54) (73) (74) (75)
(52) (332) (72) (433) (83) (543)
(322) (432) (532) (92) (552)
(522) (3322) (443) (732)
(3222) (533) (4332)
(542) (5322)
(722) (33222)
(3332)
(4322)
(5222)
(32222)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@PrimePowerQ/@#&&GCD@@#==1&]], {n, 0, 30}]
CROSSREFS
This is the relatively prime case of A023894, facs A000688, w/ 1's A023893.
For strict instead of coprime: A054685, facs A050361, with 1's A106244.
The version for factorizations instead of partitions is A354911.
A000041 counts partitions, strict A000009.
A072233 counts partitions by sum and length.
A246655 lists the prime-powers (A000961 includes 1), towers A164336.
A279784 counts twice-partitions where the latter partitions are constant.
A289509 lists numbers whose prime indices are relatively prime.
A355743 lists numbers with prime-power prime indices, squarefree A356065.
Sequence in context: A094681 A054158 A054080 * A164379 A120332 A302698
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 28 2022
STATUS
approved