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A067070 Cubes whose product of digits is a cube > 0.

%I A067070 #30 Dec 06 2024 16:24:21
%S A067070 1,8,24389,226981,9393931,11239424,17373979,36264691,66923416,
%T A067070 94818816,348913664,435519512,463684824,549353259,555412248,743677416,
%U A067070 3929352552,4982686912,5526456832,11329982936,12374478297,12681938368,15142552424
%N A067070 Cubes whose product of digits is a cube > 0.
%D A067070 Felice Russo, A set of new Smarandache Functions, Sequences and conjectures in number theory, American Research Press, Lupton USA.
%H A067070 David A. Corneth, <a href="/A067070/b067070.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%F A067070 a(n) = A067071(n)^3. - _Andrew Howroyd_, Dec 05 2024
%e A067070 24389 is in the sequence because (1) it is a cube and (2) the product of its digits is 2*4*3*8*9, = 1728 which is a cube > 0.
%t A067070 pdcQ[n_]:=Module[{pd=Times@@IntegerDigits[n]},pd>0&&IntegerQ[ Surd[ pd,3]]]; Select[Range[3000]^3,pdcQ] (* _Harvey P. Dale_, Jun 01 2015 *)
%o A067070 (PARI) isA237767(k)={my(p=vecprod(digits(k))); p && ispower(p,3)}
%o A067070 { for (m=1, 2500, if(isA237767(m^3), print1(m^3, ", "))) } \\ _Harry J. Smith_, May 04 2010
%o A067070 (PARI)
%o A067070 first(n) = {
%o A067070      my(res = List(), c, vp, i);
%o A067070      for(i = 1, oo,
%o A067070           c = i^3;
%o A067070           vp = vecprod(digits(c));
%o A067070           if(vp && ispower(vp,3),
%o A067070                listput(res, c);
%o A067070                if(#res >= n,
%o A067070                     return(Vec(res))
%o A067070                )
%o A067070           )
%o A067070      )
%o A067070 } \\ _David A. Corneth_, Dec 01 2023
%Y A067070 Intersection of A237767 and A000578.
%Y A067070 Cf. A007954, A052045, A052382, A067071.
%K A067070 nonn,base
%O A067070 1,2
%A A067070 _Amarnath Murthy_, Jan 05 2002
%E A067070 More terms from _Sascha Kurz_, Mar 23 2002
%E A067070 One further term from Luc Stevens (lms022(AT)yahoo.com), May 03 2006
%E A067070 Edited by _R. J. Mathar_, Aug 08 2008
%E A067070 Offset changed from 0 to 1 by _Harry J. Smith_, May 04 2010