A067070 - OEIS

%I #30 Dec 06 2024 16:24:21

%S 1,8,24389,226981,9393931,11239424,17373979,36264691,66923416,

%T 94818816,348913664,435519512,463684824,549353259,555412248,743677416,

%U 3929352552,4982686912,5526456832,11329982936,12374478297,12681938368,15142552424

%N Cubes whose product of digits is a cube > 0.

%D Felice Russo, A set of new Smarandache Functions, Sequences and conjectures in number theory, American Research Press, Lupton USA.

%H 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 a(n) = A067071(n)^3. - _Andrew Howroyd_, Dec 05 2024

%e 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 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 (PARI) isA237767(k)={my(p=vecprod(digits(k))); p && ispower(p,3)}

%o { for (m=1, 2500, if(isA237767(m^3), print1(m^3, ", "))) } \\ _Harry J. Smith_, May 04 2010

%o (PARI)

%o first(n) = {

%o      my(res = List(), c, vp, i);

%o      for(i = 1, oo,

%o           c = i^3;

%o           vp = vecprod(digits(c));

%o           if(vp && ispower(vp,3),

%o                listput(res, c);

%o                if(#res >= n,

%o                     return(Vec(res))

%o                )

%o           )

%o      )

%o } \\ _David A. Corneth_, Dec 01 2023

%Y Intersection of A237767 and A000578.

%Y Cf. A007954, A052045, A052382, A067071.

%K nonn,base

%O 1,2

%A _Amarnath Murthy_, Jan 05 2002

%E More terms from _Sascha Kurz_, Mar 23 2002

%E One further term from Luc Stevens (lms022(AT)yahoo.com), May 03 2006

%E Edited by _R. J. Mathar_, Aug 08 2008

%E Offset changed from 0 to 1 by _Harry J. Smith_, May 04 2010