A117690 Cubes for which both the sum of the digits and the product of the digits are squares.
0, 1, 1000, 27000, 216000, 970299, 1000000, 1860867, 2146689, 4019679, 5000211, 10077696, 14348907, 21717639, 26198073, 27000000, 27818127, 29503629, 36926037, 37933056, 57960603, 62099136, 67917312, 80621568, 84027672, 106496424, 116930169, 123505992
Offset: 0
Examples
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.
Programs
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Mathematica
okQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[Sqrt[Times@@idn]]]; Select[Range[0,500]^3,okQ] (* Harvey P. Dale, Aug 24 2011 *)
Extensions
Corrected (by inserting a(15)=26198073) by Harvey P. Dale, Aug 24 2011
More terms from Jason Yuen, Aug 30 2025