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

1, 8, 24389, 226981, 9393931, 11239424, 17373979, 36264691, 66923416, 94818816, 348913664, 435519512, 463684824, 549353259, 555412248, 743677416, 3929352552, 4982686912, 5526456832, 11329982936, 12374478297, 12681938368, 15142552424

Offset: 1

Author

Amarnath Murthy, Jan 05 2002

Keywords

• nonn
• base

Examples

			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.
		

References

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

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Crossrefs

Intersection of A237767 and A000578.

Cf. A007954, A052045, A052382, A067071.

Programs

Mathematica

pdcQ[n_]:=Module[{pd=Times@@IntegerDigits[n]},pd>0&&IntegerQ[ Surd[ pd,3]]]; Select[Range[3000]^3,pdcQ] (* Harvey P. Dale, Jun 01 2015 *)

PARI

isA237767(k)={my(p=vecprod(digits(k))); p && ispower(p,3)}
{ for (m=1, 2500, if(isA237767(m^3), print1(m^3, ", "))) } \\ Harry J. Smith, May 04 2010

PARI

first(n) = {
     my(res = List(), c, vp, i);
     for(i = 1, oo,
          c = i^3;
          vp = vecprod(digits(c));
          if(vp && ispower(vp,3),
               listput(res, c);
               if(#res >= n,
                    return(Vec(res))
               )
          )
     )
} \\ David A. Corneth, Dec 01 2023

Formula

a(n) = A067071(n)^3. - Andrew Howroyd, Dec 05 2024

Extensions

More terms from Sascha Kurz, Mar 23 2002

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

Edited by R. J. Mathar, Aug 08 2008

Offset changed from 0 to 1 by Harry J. Smith, May 04 2010