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A055400 Cube excess: difference between n and largest cube <= n.

%I A055400 #15 Dec 15 2016 02:43:19
%S A055400 0,0,1,2,3,4,5,6,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,
%T A055400 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
%U A055400 28,29,30,31,32,33,34,35,36,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
%N A055400 Cube excess: difference between n and largest cube <= n.
%H A055400 G. C. Greubel, <a href="/A055400/b055400.txt">Table of n, a(n) for n = 0..1000</a>
%F A055400 a(n) = n - A048762(n) = n - floor(n^(1/3))^3.
%F A055400 a(n) < 3*n^(2/3) for n > 0. - _Charles R Greathouse IV_, Sep 02 2015
%e A055400 a(12) = 4 because 2^3 <= 12 < 3^3 and 12 - 2^3 = 4.
%p A055400 A055400 := proc(n)
%p A055400         n-A048762(n) ;
%p A055400 end proc:
%p A055400 seq(A055400(n),n=0..80) ; # _R. J. Mathar_, Nov 06 2011
%t A055400 Array[#-Floor[Power[#, (3)^-1]]^3&,90,0] (* _Harvey P. Dale_, Jan 18 2012 *)
%o A055400 (PARI) a(n)=n-sqrtnint(n,3)^3 \\ _Charles R Greathouse IV_, Sep 02 2015
%Y A055400 Cf. A048762, A053186, A055401.
%K A055400 easy,nonn
%O A055400 0,4
%A A055400 _Henry Bottomley_, May 16 2000