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%I #20 Sep 08 2022 08:45:25
%S 0,1,8,64,125,343,512,1000,1331,2197,2744,4096,4913,6859,8000,10648,
%T 12167,15625,17576,21952,24389,29791,32768,39304,42875,50653,54872,
%U 64000,68921,79507,85184,97336,103823,117649,125000,140608,148877
%N Cubes for which the digital root is also a cube.
%C All cubes have a digital root 1,8 or 9. (except for the number 0) So this sequence contains all cubes with a digital root which is not 9.
%C This sequence is 0 union A016779 union A016791.
%H Vincenzo Librandi, <a href="/A118719/b118719.txt">Table of n, a(n) for n = 1..3000</a>
%F a(n) = (floor(3*n/2)-2)^3 for n >= 2. - _Nathaniel Johnston_, May 05 2011
%F G.f.: x^2*(1+7*x+53*x^2+40*x^3+53*x^4+7*x^5+x^6)/((1+x)^3*(1-x)^4). a(n) = A001651(n-1)^3 for n>1. - _Bruno Berselli_, May 05 2011
%F Sum_{n>=2} 1/a(n) = 26*zeta(3)/27. - _Amiram Eldar_, Dec 19 2020
%e 64 is in the sequence because (1) it is a cube and (2) the digital root 1 is also a cube.
%t Join[{0}, Table[(3*k + {1, 2})^3, {k, 0, 15}] // Flatten] (* _Amiram Eldar_, Dec 19 2020 *)
%o (Magma) [0] cat [(6*n+(-1)^n-9)^3 div 64: n in [2..37]]; // _Bruno Berselli_, May 05 2011
%o (PARI) a010888(n)=if(n, (n-1)%9+1)
%o lista(nn) = {for (n=0, nn, if (ispower(a010888(n^3), 3), print1(n^3, ", ")););} \\ _Michel Marcus_, Feb 18 2015
%Y Cf. A000578, A002117, A010888, A116978.
%K base,easy,nonn
%O 1,3
%A Luc Stevens (lms022(AT)yahoo.com), May 21 2006
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