A067071 Numbers with no zeros in their cubes such that the products of the digits of their cubes are also cubes.

1, 2, 29, 61, 211, 224, 259, 331, 406, 456, 704, 758, 774, 819, 822, 906, 1578, 1708, 1768, 2246, 2313, 2332, 2474, 3409, 3982, 4006, 4046, 4331, 4347, 4348, 4367, 4376, 4608, 4832, 4865, 4921, 5226, 5332, 5477, 5554, 5692, 5774, 5971, 6357, 6408, 6449

Offset: 1

Author

Amarnath Murthy, Jan 05 2002

Keywords

• nonn
• base

Examples

			224 belongs to this sequence as 224^3 = 11239424 and the product of the digits = 1728 = 12^3.
		

References

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

Programs

Mathematica

Do[a = Apply[Times, IntegerDigits[n^3]]; If[ a != 0 && IntegerQ[a^(1/3)], Print[n]], {n, 1, 10^4} ]
Select[Range[7000],With[{c=Times@@IntegerDigits[#^3]},c>0&&IntegerQ[CubeRoot[c]]]&] (* Harvey P. Dale, Apr 13 2025 *)

Extensions

More terms from Robert G. Wilson v, Jan 15 2002

Offset changed by Andrew Howroyd, Sep 17 2024

Definition clarified by Harvey P. Dale, Apr 13 2025