OFFSET
0,29
COMMENTS
The arithmetic and geometric mean from such partition is a positive integer. - David A. Corneth, Nov 11 2022
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..143
Wikipedia, Geometric mean
EXAMPLE
The a(30) = 2 through a(36) = 3 partitions (C = 12, G = 16):
(888222) . (99333311) (G2222222111) . (C9662) (G884)
(8844111111) (C9833) (888222111111)
(8884421) (G42222221111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Mean[#]==1+GeometricMean[#]&]], {n, 0, 30}]
PROG
(PARI) a(n) = if (n, my(nb=0, vp); forpart(p=n, vp=Vec(p); if (vecsum(vp)/#p == 1 + sqrtn(vecprod(vp), #p), nb++)); nb, 0); \\ Michel Marcus, Nov 11 2022
(Python)
from math import prod
from sympy import divisors, integer_nthroot
from sympy.utilities.iterables import partitions
def A358331(n):
divs = {d:n//d-1 for d in divisors(n, generator=True)}
return sum(1 for s, p in partitions(n, m=max(divs, default=0), size=True) if s in divs and (t:=integer_nthroot(prod(a**b for a, b in p.items()), s))[1] and divs[s]==t[0]) # Chai Wah Wu, Sep 24 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 09 2022
EXTENSIONS
a(61)-a(80) from Giorgos Kalogeropoulos, Nov 11 2022
a(81)-a(84) from Chai Wah Wu, Sep 24 2023
STATUS
approved