OFFSET
1,2
COMMENTS
What is the asymptotic growth of this sequence?
Answer: a(n) ~ kn, where k = 1/A175475. That is, about 4.8% of numbers are in this sequence. - Charles R Greathouse IV, Jul 14 2014
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
Solutions to A006530(n) <= n^(1/3).
EXAMPLE
378 = 2 * 3^3 * 7 is a term of the sequence since 7 < 7.23... = 378^(1/3).
MAPLE
filter:= n ->
evalb(max(seq(f[1], f=ifactors(n)[2]))^3 <= n):
select(filter, [$1..1000]); # Robert Israel, Jul 14 2014
MATHEMATICA
ffi[x_] := Flatten[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; lf[x_] := Length[FactorInteger[x]]; ma[x_] := Max[ba[x]]; Do[If[ !Greater[ma[n], gy=n^(1/3)//N]&&!PrimeQ[n], Print[n(*, {gy, ma[n]}}*)]], {n, 1, 1000}]
Select[Range[1000], (FactorInteger[#][[-1, 1]])^3 <= # &] (* T. D. Noe, Sep 14 2011 *)
PROG
(PARI) is(n)=my(f=factor(n)[, 1]); f[#f]^3<=n \\ Charles R Greathouse IV, Sep 14 2011
(Python)
from sympy import primefactors
def ok(n):
if n==1 or max(primefactors(n))**3<=n: return True
else: return False
print([n for n in range(1, 1001) if ok(n)]) # Indranil Ghosh, Apr 23 2017
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Labos Elemer, Nov 21 2003
STATUS
approved