A059172 Numbers k such that k/rad(k) > sqrt(k) where rad(k) is the largest squarefree number dividing k.

8, 16, 27, 32, 48, 54, 64, 72, 81, 96, 108, 125, 128, 144, 160, 162, 192, 200, 216, 224, 243, 250, 256, 288, 320, 324, 343, 375, 384, 392, 400, 405, 432, 448, 486, 500, 512, 567, 576, 625, 640, 648, 675, 686, 704, 729, 768, 784, 800, 832, 864, 896, 960, 968

Offset: 1

Author

Leroy Quet, Feb 14 2001

Keywords

• nonn

Comments

Numbers k which have measure of smoothness J bigger as 2. Where J = log(k)/log(rad(k)), where rad(k) is product of distinct prime divisors of k. - Artur Jasinski, Feb 02 2010

Examples

			48 is included because 6 is largest squarefree to divide 48 and 48 /6 = 8 > sqrt(48).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A003557, A007947.

Programs

Mathematica

aa = {}; Do[kk = FactorInteger[c]; nn = 1; Do[nn = nn*kk[[n]][[1]], {n, 1, Length[kk]}]; If[Log[c]/Log[nn] >= 2,AppendTo[aa, c]], {c, 2, 1000}]; aa (* Artur Jasinski, Feb 02 2010 *)
Select[Range[1000],#/Last[Select[Divisors[#],SquareFreeQ]]>Sqrt[#]&] (* Harvey P. Dale, Dec 14 2017 *)