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A343382 Number of strict integer partitions of n with either (1) no part dividing all the others or (2) no part divisible by all the others. 17
1, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 9, 9, 13, 18, 21, 26, 34, 38, 48, 57, 67, 81, 99, 110, 133, 157, 183, 211, 250, 282, 330, 380, 437, 502, 575, 648, 748, 852, 967, 1095, 1250, 1405, 1597, 1801, 2029, 2287, 2579, 2883, 3245, 3638, 4077, 4557, 5107, 5691, 6356 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
Alternative name: Number of strict integer partitions of n that are either (1) empty, or (2) have smallest part not dividing all the others, or (3) have greatest part not divisible by all the others.
LINKS
EXAMPLE
The a(0) = 1 through a(11) = 9 partitions (empty columns indicated by dots):
() . . . . (3,2) (3,2,1) (4,3) (5,3) (5,4) (6,4) (6,5)
(5,2) (4,3,1) (7,2) (7,3) (7,4)
(5,2,1) (4,3,2) (5,3,2) (8,3)
(5,3,1) (5,4,1) (9,2)
(7,2,1) (5,4,2)
(4,3,2,1) (6,3,2)
(6,4,1)
(7,3,1)
(5,3,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], #=={}||UnsameQ@@#&&!And@@IntegerQ/@(#/Min@@#)||UnsameQ@@#&&!And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
CROSSREFS
The first condition alone gives A341450.
The non-strict version is A343346 (Heinz numbers: A343343).
The second condition alone gives A343377.
The strict complement is A343378.
The version for "and" instead of "or" is A343379.
A000005 counts divisors.
A000009 counts strict partitions.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
A018818 counts partitions into divisors (strict: A033630).
A167865 counts strict chains of divisors > 1 summing to n.
A339564 counts factorizations with a selected factor.
Sequence in context: A036561 A334860 A082976 * A242407 A047419 A135205
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 16 2021
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)