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A366750
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Number of strict integer partitions of n into odd parts with a common divisor > 1.
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2
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0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 1, 1, 3, 1, 0, 2, 0, 1, 3, 1, 0, 3, 2, 1, 4, 1, 1, 5, 0, 1, 5, 1, 2, 5, 1, 1, 5, 2, 2, 6, 0, 1, 9, 1, 0, 9, 0, 3, 9, 1, 1, 9, 5, 1, 11, 1, 0, 15, 1, 2, 13, 1, 5, 14, 0, 1, 18
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OFFSET
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0,25
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LINKS
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EXAMPLE
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The a(n) partitions for n = 3, 24, 30, 42, 45, 57, 60:
(3) (15,9) (21,9) (33,9) (45) (57) (51,9)
(21,3) (25,5) (35,7) (33,9,3) (45,9,3) (55,5)
(27,3) (39,3) (21,15,9) (27,21,9) (57,3)
(27,15) (25,15,5) (33,15,9) (33,27)
(27,15,3) (33,21,3) (35,25)
(39,15,3) (39,21)
(45,15)
(27,21,9,3)
(33,15,9,3)
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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 A366750(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, Nov 02 2023
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CROSSREFS
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This is the case of A000700 with a common divisor.
A113685 counts partitions by sum of odd parts, rank statistic A366528.
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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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