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Cubes whose digit sum is also a cube.
4

%I #29 Oct 23 2024 01:28:55

%S 0,1,8,125,512,1000,1331,8000,19683,35937,46656,59319,74088,125000,

%T 157464,185193,328509,373248,421875,474552,512000,592704,658503,

%U 804357,1000000,1030301,1157625,1259712,1331000,1367631,1481544,2460375,2628072,3176523,4251528,4492125,4741632,5268024,5545233,8000000,10503459,10941048,11390625,11852352,12326391,12812904,17173512,19034163,19683000,20346417

%N Cubes whose digit sum is also a cube.

%D Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press, 2000.

%F a(n) = A237525(n)^3.

%t Select[Range[0, 200]^3, IntegerQ[(Plus@@IntegerDigits[ #])^(1/3)]&] (* _Dean Hickerson_, Apr 08 2002 *)

%t k=0;Monitor[Parallelize[While[True,If[And[IntegerQ[k^(1/3)],IntegerQ[Total[IntegerDigits[k]]^(1/3)]],Print[k]]; k++]; k], k] (* _J.W.L. (Jan) Eerland_, Sep 30 2024 *)

%o (PARI) v=List();for(n=0,1e2,if(ispower(sumdigits(n^3),3), listput(v, n^3))); Vec(v) \\ _Charles R Greathouse IV_, Sep 20 2012

%Y Intersection of A059094 and A000578.

%Y Cf. A237525.

%K easy,base,nonn

%O 1,3

%A _Felice Russo_, Feb 25 2000

%E More terms from _James A. Sellers_, Feb 28 2000

%E Edited by _N. J. A. Sloane_, Apr 11 2009 at the suggestion of _Eric Angelini_

%E a(33)-a(50) from _J.W.L. (Jan) Eerland_, Sep 30 2024