OFFSET
0,3
EXAMPLE
The a(6) = 4 through a(9) = 15 compositions:
(6) (7) (8) (9)
(33) (124) (44) (333)
(222) (142) (2222) (1224)
(111111) (214) (11111111) (1242)
(241) (1422)
(412) (2124)
(421) (2142)
(1111111) (2214)
(2241)
(2412)
(2421)
(4122)
(4212)
(4221)
(111111111)
MATHEMATICA
Table[Length[Select[Join @@ Permutations/@IntegerPartitions[n], IntegerQ[GeometricMean[#]]&]], {n, 0, 15}]
PROG
(Python)
from math import prod, factorial
from sympy import integer_nthroot
from sympy.utilities.iterables import partitions
def A357710(n): return sum(factorial(s)//prod(factorial(d) for d in p.values()) for s, p in partitions(n, size=True) if integer_nthroot(prod(a**b for a, b in p.items()), s)[1]) if n else 0 # Chai Wah Wu, Sep 24 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 15 2022
EXTENSIONS
More terms from David A. Corneth, Oct 17 2022
STATUS
approved