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

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A000290, A000578.

Sequence in context: A004632 A277397 A250449 * A186936 A185747 A234787

Adjacent sequences: A117687 A117688 A117689 * A117691 A117692 A117693

Keyword

nonn,base

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 12 2006

Extensions

Corrected (by inserting a(15)=26198073) by Harvey P. Dale, Aug 24 2011

Status

approved