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A090081
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Cube root-smooth numbers: numbers n such that largest prime factor of n does not exceed cube root of n.
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1
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1, 8, 16, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 125, 128, 135, 144, 150, 160, 162, 180, 192, 200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 343, 350, 360, 375, 378, 384, 392, 400, 405, 420, 432, 441, 448, 450, 480, 486, 490, 500, 504, 512, 525
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| What is the asymptotic growth of this sequence?
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LINKS
| Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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FORMULA
| Solutions to A006530(n) <= n^(1/3).
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EXAMPLE
| 378 = 2 * 3^3 * 7 is a member of the sequence since 7 < 7.23... = 378^(1/3).
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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 *)
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PROG
| (PARI) is(n)=my(f=factor(n)[, 1]); f[#f]^3<=n \\ Charles R Greathouse IV, Sep 14 2011
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CROSSREFS
| Cf. A063763, A001248, A048098, A036966, A054744, A059172, A068936, A076405, A076467.
Sequence in context: A074750 A190519 A180861 * A059172 A107606 A036966
Adjacent sequences: A090078 A090079 A090080 * A090082 A090083 A090084
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Nov 21 2003
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