OFFSET
1,2
COMMENTS
The analogous sequence with squarefree numbers is A072048.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Zhu Weiyi, On the cube free number sequences, Smarandache Notions J., Vol. 14 (2004), pp. 199-202.
FORMULA
Sum_{k=1..n} a(k) = (36*c_1/Pi^4) * n * (log(n) + (2*gamma - 1) - 24*zeta'(2)/Pi^2 - 4*c_2) + O(n^(1/2 + eps)), where c_1 = Product_{p prime} ((p^2+2*p+3)/(p+1)^2) = 1.58095136661854869148023... and c_2 = Sum_{p prime} p*log(p)/((p+1)*(p^2+2*p+3)) = 0.229224... (Weiyi, 2004).
MATHEMATICA
DivisorSigma[0, Select[Range[100], Max[FactorInteger[#][[;; , 2]]] < 3 &]]
PROG
(Python)
from sympy import mobius, integer_nthroot, divisor_count
def A358040(n):
def f(x): return n+x-sum(mobius(k)*(x//k**3) for k in range(1, integer_nthroot(x, 3)[0]+1))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return divisor_count(m) # Chai Wah Wu, Aug 06 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 29 2022
STATUS
approved