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A371180
Number of strict integer partitions of n with fewer parts than distinct divisors of parts.
3
0, 0, 1, 1, 1, 3, 2, 4, 4, 7, 8, 10, 12, 15, 19, 22, 29, 33, 40, 47, 57, 68, 81, 95, 110, 129, 152, 178, 207, 240, 277, 317, 365, 422, 486, 558, 632, 723, 824, 940, 1067, 1210, 1371, 1544, 1751, 1977, 2233, 2508, 2820, 3162, 3555, 3983, 4465, 4990, 5571, 6224
OFFSET
0,6
EXAMPLE
The strict partition (6,4,2,1) has 4 parts and 5 distinct divisors of parts {1,2,3,4,5}, so is counted under a(13).
The a(2) = 1 through a(11) = 10 partitions:
(2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
(3,2) (4,2) (4,3) (5,3) (5,4) (6,4) (6,5)
(4,1) (5,2) (6,2) (6,3) (7,3) (7,4)
(6,1) (4,3,1) (7,2) (8,2) (8,3)
(8,1) (9,1) (9,2)
(4,3,2) (5,3,2) (10,1)
(6,2,1) (5,4,1) (5,4,2)
(6,3,1) (6,3,2)
(6,4,1)
(8,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[Union[#]] < Length[Union@@Divisors/@#]&]], {n, 0, 30}]
CROSSREFS
The LHS is represented by A001221, distinct case of A001222.
The RHS is represented by A370820, for prime factors A303975.
The version for equality is A371128.
The non-strict version is A371132, ranks A371179.
The non-strict complement is A371178, ranks A371177.
A000005 counts divisors.
A000041 counts integer partitions, strict A000009.
A008284 counts partitions by length.
Sequence in context: A367219 A241412 A241445 * A147604 A095401 A309511
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2024
STATUS
approved