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a(n)=n^2 times nearest cube to n^2.
1

%I #12 May 13 2020 17:05:26

%S 0,1,4,72,128,675,972,3136,4096,5184,12500,15125,18000,21125,42336,

%T 48600,55296,99127,111132,123823,137200,225792,247808,270848,294912,

%U 455625,492804,531441,571536,613089,900000,961000,1024000,1089000

%N a(n)=n^2 times nearest cube to n^2.

%H Harvey P. Dale, <a href="/A077112/b077112.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A000290(n)*A077110(n).

%t ntnc[n_]:=Module[{n2=n^2,a,b,a3,b3},a=Floor[Power[n2,(3)^-1]]; b=a+1; a3=a^3; b3=b^3;If[n2-a3<b3-n2,n2 a3,n2 b3]]; Array[ntnc,40,0] (* _Harvey P. Dale_, Jan 06 2012 *)

%t nic[n_]:=Module[{n2=n^2,c},c=Floor[Surd[n2,3]];n2*Nearest[{c^3,(c+1)^3}, n2]]; Join[{0,1},Array[nic,40,2]]//Flatten//Union (* _Harvey P. Dale_, May 13 2020 *)

%K nonn,nice

%O 0,3

%A _Reinhard Zumkeller_, Oct 29 2002