OFFSET
0,5
EXAMPLE
The a(1) = 1 through a(8) = 6 partitions:
(1) (11) (111) (31) (311) (51) (331) (53)
(1111) (11111) (3111) (511) (71)
(111111) (31111) (3311)
(1111111) (5111)
(311111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], #=={}||And@@OddQ/@#&&GCD@@#==1&]], {n, 0, 30}]
PROG
(Python)
from math import gcd
from sympy.utilities.iterables import partitions
def A366843(n): return sum(1 for p in partitions(n) if all(d&1 for d in p) and gcd(*p)==1) # Chai Wah Wu, Oct 30 2023
CROSSREFS
Allowing even parts gives A000837.
A000740 counts relatively prime compositions.
A168532 counts partitions by gcd.
A366842 counts partitions whose odd parts have a common divisor > 1.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 28 2023
STATUS
approved