OFFSET
0,12
EXAMPLE
The a(11) = 2 through a(18) = 8 partitions:
(5,4) . (6,5) (6,5) (7,6) (7,5) (7,4) (7,5)
(7,3) (7,4) (8,5) (9,4) (7,6) (7,6) (8,7)
(7,5) (9,4) (9,5) (8,5) (10,7)
(8,3) (10,3) (11,3) (8,7) (11,4)
(9,5) (11,5)
(9,7) (12,5)
(10,3) (13,4)
(11,4) (7,5,5)
(11,5)
(13,3)
(7,4,4)
(10,3,3)
MATHEMATICA
combsu[n_, y_]:=With[{s=Table[{k, i}, {k, Union[y]}, {i, 0, Floor[n/k]}]}, Select[Tuples[s], Total[Times@@@#]==n&]];
Table[Length[Select[Join@@IntegerPartitions/@Range[n-1], GCD@@#==1&&combsu[n, #]=={}&]], {n, 0, 20}]
PROG
(Python)
from math import gcd
from sympy.utilities.iterables import partitions
def A365382(n):
a = {tuple(sorted(set(p))) for p in partitions(n)}
return sum(1 for m in range(1, n) for b in partitions(m) if gcd(*b.keys()) == 1 and not any(set(d).issubset(set(b)) for d in a)) # Chai Wah Wu, Sep 13 2023
CROSSREFS
This is the relatively prime case of A365378.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 08 2023
EXTENSIONS
a(21)-a(45) from Chai Wah Wu, Sep 13 2023
STATUS
approved