This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090081 #46 Jun 30 2025 18:03:06
%S A090081 1,8,16,27,32,36,48,54,64,72,81,96,108,125,128,135,144,150,160,162,
%T A090081 180,192,200,216,225,240,243,250,256,270,288,300,320,324,343,350,360,
%U A090081 375,378,384,392,400,405,420,432,441,448,450,480,486,490,500,504,512,525
%N A090081 Cube root-smooth numbers: numbers k whose largest prime factor does not exceed the cube root of k.
%C A090081 What is the asymptotic growth of this sequence?
%C A090081 Answer: a(n) ~ k*n, where k = 1/A175475. That is, about 4.8% of numbers are in this sequence. - _Charles R Greathouse IV_, Jul 14 2014
%H A090081 Charles R Greathouse IV, <a href="/A090081/b090081.txt">Table of n, a(n) for n = 1..10000</a>
%F A090081 Solutions to A006530(n) <= n^(1/3).
%e A090081 378 = 2 * 3^3 * 7 is a term of the sequence since 7 < 7.23... = 378^(1/3).
%p A090081 filter:= n ->
%p A090081 evalb(max(seq(f[1],f=ifactors(n)[2]))^3 <= n):
%p A090081 select(filter, [$1..1000]); # _Robert Israel_, Jul 14 2014
%t A090081 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}]
%t A090081 Select[Range[1000], (FactorInteger[#][[-1,1]])^3 <= # &] (* _T. D. Noe_, Sep 14 2011 *)
%t A090081 Select[Range[1000],FactorInteger[#][[-1,1]]<=CubeRoot[#]&] (* _Harvey P. Dale_, Jun 30 2025 *)
%o A090081 (PARI) is(n)=my(f=factor(n)[,1]);f[#f]^3<=n \\ _Charles R Greathouse IV_, Sep 14 2011
%o A090081 (Python)
%o A090081 from sympy import primefactors
%o A090081 def ok(n):
%o A090081 if n==1 or max(primefactors(n))**3<=n: return True
%o A090081 else: return False
%o A090081 print([n for n in range(1, 1001) if ok(n)]) # _Indranil Ghosh_, Apr 23 2017
%Y A090081 Cf. A063763, A001248, A048098, A036966, A054744, A059172, A068936, A076405, A076467, A006530, A175475.
%K A090081 nonn,nice
%O A090081 1,2
%A A090081 _Labos Elemer_, Nov 21 2003