OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
For n > 35, a(n) < 7n. Asymptotically, a(n) ~ kn with k = zeta(3)/(zeta(3)-1) = 5.949... . - Charles R Greathouse IV, Oct 16 2015 [Corrected by Amiram Eldar, Aug 31 2024]
Sum_{n>=1} 1/a(n)^s = 1 + zeta(s) - zeta(3*s) - zeta(s)/zeta(3*s), for s > 1. - Amiram Eldar, Aug 31 2024
MATHEMATICA
With[{m = 10}, Select[Complement[Range[m^3], Range[m]^3], AnyTrue[FactorInteger[#][[;; , 2]], #1 > 2 &] &]] (* Amiram Eldar, Aug 31 2024 *)
PROG
(PARI) is(n)=my(f=factor(n)[, 2]); f%3 && vecmax(f)>2 \\ Charles R Greathouse IV, Oct 16 2015
(Python)
from sympy import integer_nthroot, mobius
def A074451(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
kmin = kmax >> 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n-1+(m:=integer_nthroot(x, 3)[0])+sum(mobius(k)*(x//k**3) for k in range(1, m+1))
return bisection(f, n, n) # Chai Wah Wu, Jun 05 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 25 2002
STATUS
approved