%I
%S 16,32,48,64,80,81,96,112,128,144,160,162,176,192,208,224,240,243,256,
%T 272,288,304,320,324,336,352,368,384,400,405,416,432,448,464,480,486,
%U 496,512,528,544,560,567,576,592,608,624,625,640,648,656,672,688,704
%N Biquadrateful numbers.
%C The convention in the OEIS is that squareful, cubeful (A046099), biquadrateful, ... mean the same as "not squarefree" etc., while 2 or squarefull, 3 or cubefull (A036966), 4full (A036967) are used for Golomb's notion of powerful numbers (A001694, see references there), when each prime factor occurs to a power > 1.  _M. F. Hasler_, Feb 12 2008
%C Also solutions to equation tau_{3}(n)=0, where tau_{3} is A007428.  _Enrique Pérez Herrero_, Jan 19 2013
%C Sum_{n>0} 1/a(n)^s = Zeta(s)  Zeta(s)/Zeta(4s).  _Enrique Pérez Herrero_, Jan 21 2013
%C A051903(a(n)) > 3.  _Reinhard Zumkeller_, Sep 03 2015
%H T. D. Noe, <a href="/A046101/b046101.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Biquadratefree.html">Biquadratefree.</a>
%t lst={};Do[a=0;Do[If[FactorInteger[m][[n, 2]]>3, a=1], {n, Length[FactorInteger[m]]}];If[a==1, AppendTo[lst, m]], {m, 10^3}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 15 2008 *)
%t Select[Range[1000],Max[Transpose[FactorInteger[#]][[2]]]>3&] (* _Harvey P. Dale_, May 25 2014 *)
%o (Haskell)
%o a046101 n = a046101_list !! (n1)
%o a046101_list = filter ((> 3) . a051903) [1..]
%o  _Reinhard Zumkeller_, Sep 03 2015
%o (PARI) is(n)=n>9 && vecmax(factor(n)[,2])>3 \\ _Charles R Greathouse IV_, Sep 03 2015
%Y Cf. A046100, A046099, A036967, A001694, A051903.
%K nonn
%O 1,1
%A _Eric W. Weisstein_
