OFFSET
0,9
EXAMPLE
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)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@OddQ/@#&&UnsameQ@@#&&GCD@@#==1&]], {n, 0, 30}]
PROG
(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
CROSSREFS
This is the relatively prime case of A000700.
The pairwise coprime version is the odd-part case of A007360.
Allowing even parts gives A078374.
The halved even version is A078374 aerated.
A168532 counts partitions by gcd.
A366842 counts partitions whose odd parts have a common divisor > 1.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 29 2023
EXTENSIONS
More terms from Chai Wah Wu, Oct 30 2023
STATUS
approved