

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
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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

For parts > 1 instead of gcd > 1 we have A087897.
For gcd = 1 instead of gcd > 1 we have A366843.
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.
A366842 counts partitions whose odd parts have a common divisor > 1.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



