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A366852 Number of integer partitions of n into odd parts with a common divisor > 1. 5
0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 4, 0, 1, 4, 1, 2, 6, 1, 1, 6, 3, 1, 8, 2, 1, 13, 1, 0, 13, 1, 7, 15, 1, 1, 19, 6, 1, 25, 1, 2, 33, 1, 1, 32, 5, 10, 39, 2, 1, 46, 14, 6, 55, 1, 1, 77, 1, 1, 82, 0, 20, 92, 1, 2, 105, 31, 1, 122, 1, 1, 166, 2, 16, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
LINKS
EXAMPLE
The a(n) partitions for n = 3, 9, 15, 21, 25, 27:
(3) (9) (15) (21) (25) (27)
(3,3,3) (5,5,5) (7,7,7) (15,5,5) (9,9,9)
(9,3,3) (9,9,3) (5,5,5,5,5) (15,9,3)
(3,3,3,3,3) (15,3,3) (21,3,3)
(9,3,3,3,3) (9,9,3,3,3)
(3,3,3,3,3,3,3) (15,3,3,3,3)
(9,3,3,3,3,3,3)
(3,3,3,3,3,3,3,3,3)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@OddQ/@#&&GCD@@#>1&]], {n, 15}]
PROG
(Python)
from math import gcd
from sympy.utilities.iterables import partitions
def A366852(n): return sum(1 for p in partitions(n) if all(d&1 for d in p) and gcd(*p)>1) # Chai Wah Wu, Nov 02 2023
CROSSREFS
Allowing even parts gives A018783, complement A000837.
For parts > 1 instead of gcd > 1 we have A087897.
For gcd = 1 instead of gcd > 1 we have A366843.
The strict case is A366750, with evens A303280.
The strict complement is A366844, with evens A078374.
A000041 counts integer partitions, strict A000009 (also into odd parts).
A000700 counts strict partitions into odd parts.
A113685 counts partitions by sum of odd parts, rank statistic A366528.
A168532 counts partitions by gcd.
A366842 counts partitions whose odd parts have a common divisor > 1.
Sequence in context: A035693 A328818 A361498 * A318666 A301391 A068696
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 01 2023
EXTENSIONS
More terms from Chai Wah Wu, Nov 02 2023
a(0)=0 prepended by Alois P. Heinz, Jan 11 2024
STATUS
approved

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Last modified July 19 16:24 EDT 2024. Contains 374410 sequences. (Running on oeis4.)