OFFSET
1,3
EXAMPLE
The a(2) = 1 through a(5) = 10 partitions:
{1} {1} {1} {1}
{1,2} {2} {1,2}
{1,2} {1,3}
{1,3} {1,4}
{2,3} {2,3}
{1,2,3} {1,2,3}
{1,2,4}
{1,3,4}
{2,3,4}
{1,2,3,4}
MATHEMATICA
combs[n_, y_]:=With[{s=Table[{k, i}, {k, y}, {i, 0, Floor[n/k]}]}, Select[Tuples[s], Total[Times@@@#]==n&]];
Table[Length[Select[Subsets[Range[n-1]], combs[n, #]!={}&]], {n, 5}]
PROG
(Python)
from itertools import combinations
from sympy.utilities.iterables import partitions
def A365542(n):
a = {tuple(sorted(set(p))) for p in partitions(n)}
return sum(1 for m in range(1, n) for b in combinations(range(1, n), m) if any(set(d).issubset(set(b)) for d in a)) # Chai Wah Wu, Sep 12 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 09 2023
EXTENSIONS
More terms from Alois P. Heinz, Sep 13 2023
STATUS
approved