OFFSET
1,2
COMMENTS
Superset of A005117 and A067259. The first numbers not in the sequence are 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, 704, 729 etc. [R. J. Mathar, Oct 11 2008]
This sequence has an asymptotic density of about 0.98270. - David A. Corneth, Nov 05 2017
From Amiram Eldar, Mar 20 2021: (Start)
The asymptotic density of this sequence is 1/zeta(6) = 1/A013664 = 945/Pi^6 = 0.9829525922...
The Schnirelmann density of this sequence is 6165/6272 (Orr, 1969). (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Richard C. Orr, On the Schnirelmann density of the sequence of k-free integers, Journal of the London Mathematical Society, Vol. 1, No. 1 (1969), pp. 313-319.
FORMULA
{n: A051903(n) <= 5}. [R. J. Mathar, Oct 11 2008, corrected Oct 19 2008]
MAPLE
select(n -> max(seq(f[2], f=ifactors(n)[2]))<=5, [$1..1000]); # Robert Israel, Nov 05 2017
MATHEMATICA
lst={}; Do[a=0; Do[If[FactorInteger[m][[n, 2]]>5, a=1], {n, Length[FactorInteger[m]]}]; If[a!=1, AppendTo[lst, m]], {m, 2*5!}]; lst
Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]] , #1 < 6 & ] &] (* Amiram Eldar, Mar 20 2021 *)
PROG
(Python)
from sympy import mobius, integer_nthroot
def A144972(n):
def f(x): return n+x-sum(mobius(k)*(x//k**6) for k in range(1, integer_nthroot(x, 6)[0]+1))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return m # Chai Wah Wu, Aug 05 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Sep 27 2008
STATUS
approved