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A059172 Numbers k such that k/rad(k) > sqrt(k) where rad(k) is the largest squarefree number dividing k. 35

%I #24 Mar 10 2020 10:24:33

%S 8,16,27,32,48,54,64,72,81,96,108,125,128,144,160,162,192,200,216,224,

%T 243,250,256,288,320,324,343,375,384,392,400,405,432,448,486,500,512,

%U 567,576,625,640,648,675,686,704,729,768,784,800,832,864,896,960,968

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

%C 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

%H Amiram Eldar, <a href="/A059172/b059172.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

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

%t 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 *)

%t Select[Range[1000],#/Last[Select[Divisors[#],SquareFreeQ]]>Sqrt[#]&] (* _Harvey P. Dale_, Dec 14 2017 *)

%Y Cf. A003557, A007947.

%K nonn

%O 1,1

%A _Leroy Quet_, Feb 14 2001

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)