A164883 Cubes with the property that the sum of the cubes of the digits is also a cube.

0, 1, 8, 1000, 8000, 474552, 1000000, 1643032, 8000000, 13312053, 27818127, 125751501, 474552000, 1000000000, 1015075125, 1121622319, 1256216039, 1501123625, 1643032000, 3811036328, 8000000000, 11000295424, 13312053000

Offset: 1

Author

Amarnath Murthy, Apr 21 2001

Keywords

• nonn
• base

Comments

It is known (Murthy 2001) that the sequence is infinite. (1) The number {3(10^(k+2)+1)}^3 for all k produces such numbers. (2) Less trivially, {10^(n+2) - 4}^3 is a member of this sequence for n = 4*{(10^(3k)-1)/27}-1, for all k, for which the sum of the cubes of the digits is {6*10^k}^3.

Examples

			474552 = 78^3 is a term since 4^3+7^3+4^3+5^3+5^3+2^3 = 729 = 9^3.
		

References

• Amarnath Murthy, Smarandache Fermat Additive Cubic Sequence, 2011. (To be published in the Smarandache Notions Journal.)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

R:= NULL: count:= 0:
for x from 0 while count < 100 do
  v:= x^3;
  t:= add(s^3,s=convert(v,base,10));
  if surd(t,3)::integer then
       R:= R, v; count:= count+1;
  fi;
od:
R; # Robert Israel, Apr 15 2025

Mathematica

Select[Range[0,2500]^3,IntegerQ[Total[IntegerDigits[#]^3]^(1/3)]&] (* Harvey P. Dale, Jun 03 2012 *)

Extensions

Corrected and extended by Gaurav Kumar, Aug 29 2009