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A370806
Number of non-strict condensed integer partitions of n.
5
0, 0, 0, 0, 1, 0, 1, 1, 3, 2, 4, 4, 8, 9, 11, 14, 19, 24, 29, 39, 47, 58, 70, 85, 104, 129, 152, 184, 223, 264, 313
OFFSET
0,9
COMMENTS
These are non-strict partitions such that it is possible to choose a different divisor of each part.
EXAMPLE
The a(4) = 1 through a(13) = 9 partitions:
(22) . (33) (322) (44) (441) (55) (443) (66) (544)
(332) (522) (433) (533) (444) (553)
(422) (442) (722) (552) (661)
(622) (4322) (633) (733)
(822) (922)
(4332) (4432)
(4431) (5332)
(5322) (5422)
(6322)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !UnsameQ@@# && Length[Select[Tuples[Divisors/@#], UnsameQ@@#&]]>0&]], {n, 0, 30}]
CROSSREFS
This is the non-strict case of A239312, complement A370320.
These partitions have as ranks the nonsquarefree terms of A368110.
A000005 counts divisors.
A000041 counts integer partitions, strict A000009.
A355731 counts choices of a divisor of each prime index, firsts A355732.
A370592 counts factor-choosable partitions, complement A370593.
A370814 counts condensed factorizations, complement A370813.
Sequence in context: A095401 A309511 A195472 * A240538 A326923 A365613
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 04 2024
STATUS
approved