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%I #7 Nov 21 2013 12:48:57
%S 0,1,1000,27000,216000,970299,1000000,1860867,2146689,4019679,5000211,
%T 10077696,14348907,21717639,26198073,27000000,27818127,29503629,
%U 36926037,37933056,57960603,62099136,67917312,80621568,84027672
%N Cubes for which both the sum of the digits and the product of the digits are squares.
%e 2146689 is in the sequence because it is a cube and (1)the sum of its digits 2+1+4+6+6+8+9=36 is a square and (2)the product of its digits 2*1*4*6*6*8*9=20736 is also a square.
%t okQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[Sqrt[Times@@idn]]]; Select[Range[0,450]^3,okQ] (* _Harvey P. Dale_, Aug 24 2011 *)
%Y Cf. A000290, A000578.
%K nonn,base
%O 0,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 12 2006
%E Corrected (by inserting a(15)=26198073) by Harvey P. Dale, Aug 24 2011
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