%I A140823
%S A140823 2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,
%T A140823 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A140823 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74
%N A140823 Natural numbers which are not perfect fourth powers.
%C A140823 First differs from A046100 at {32, 48, 64, 80, 96, 112, 144, 160, 162, 
               ...}. What formula does dos Reis provide analogous to the formulae 
               for nonsquares A000037(n) = n + [1/2 + sqrt(n)] and noncubes A007412(n) 
               = n + [(n + [n^{1/3}])^{1/3}]? The partial sum of nonbiquadratic 
               numbers < n is (the sum of all natural numbers < n) - (the sum of 
               4th powers k^4 < n) = (n*(n-1)/2) - A000538(j < n^(1/4)) = (n*(n-1)/
               2) - (j*(1+j)*(1+2*j)*(-1+3*j+3*j^2)/30) for j < [n^(1/4)].
%D A140823 A. J. dos Reis and D. M. Silberger, Generating nonpowers by formula, 
               Math. Mag., 63 (1990), 53-55.
%F A140823 {a(n) in A000027 and a(n) not in A000583} = (n in A000027 and a(n) <> 
               k^4}.
%Y A140823 Cf. A000037, A000583, A007412, A046100.
%Y A140823 Sequence in context: A023770 A023797 A032951 this_sequence A115063 A013938 
               A023809
%Y A140823 Adjacent sequences: A140820 A140821 A140822 this_sequence A140824 A140825 
               A140826
%K A140823 easy,nonn
%O A140823 1,1
%A A140823 Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 17 2008