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A366844
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Number of strict integer partitions of n into odd relatively prime parts.
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10
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0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 2, 3, 3, 5, 4, 4, 5, 6, 7, 8, 8, 9, 11, 12, 12, 15, 16, 15, 19, 23, 23, 26, 28, 30, 34, 37, 38, 44, 48, 48, 56, 62, 63, 72, 77, 82, 92, 96, 102, 116, 124, 128, 142, 155, 162, 178, 191, 200, 222, 236, 246, 276, 291, 303, 334
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OFFSET
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0,9
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LINKS
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EXAMPLE
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The a(n) partitions for n = 1, 8, 14, 17, 16, 20, 21:
(1) (5,3) (9,5) (9,5,3) (9,7) (11,9) (9,7,5)
(7,1) (11,3) (9,7,1) (11,5) (13,7) (11,7,3)
(13,1) (11,5,1) (13,3) (17,3) (11,9,1)
(13,3,1) (15,1) (19,1) (13,5,3)
(7,5,3,1) (9,7,3,1) (13,7,1)
(11,5,3,1) (15,5,1)
(17,3,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], And@@OddQ/@#&&UnsameQ@@#&&GCD@@#==1&]], {n, 0, 30}]
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PROG
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(Python)
from math import gcd
from sympy.utilities.iterables import partitions
def A366844(n): return sum(1 for p in partitions(n) if all(d==1 for d in p.values()) and all(d&1 for d in p) and gcd(*p)==1) # Chai Wah Wu, Oct 30 2023
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CROSSREFS
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This is the relatively prime case of A000700.
The pairwise coprime version is the odd-part case of A007360.
The halved even version is A078374 aerated.
The complement is counted by the strict case of A366852, with evens A018783.
A113685 counts partitions by sum of odd parts, rank statistic A366528.
A366842 counts partitions whose odd parts have a common divisor > 1.
Cf. A007359, A047967, A055922, A066208, A116598, A239261, A302697, A337485, A365067, A366845, A366848.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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