A153185 Numbers n such that Q(n) + Q(n^2) + Q(n^3) is a perfect square where Q(n) is the sum of the digits of n.

9, 18, 45, 90, 171, 180, 207, 279, 297, 396, 414, 450, 459, 486, 567, 576, 693, 702, 729, 738, 747, 900, 918, 954, 981, 1062, 1134, 1161, 1197, 1206, 1215, 1233, 1323, 1332, 1341, 1431, 1449, 1467, 1485, 1494, 1503, 1656, 1710, 1737, 1755, 1800, 1908, 2007

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Pedro Henrique O. Pantoja, Problem 3506, Crux Mathematicorum, February 2010, Volume 36 Number 1, p. 45.

Example

747 is a member: Q(747) = 7+4+7 = 18, Q(747^2) = Q(558009) = 5+5+8+0+0+9 = 27, Q(747^3) = Q(416832723) = 4+1+6+8+3+2+7+2+3 = 36, Q(747) + Q(747^2) + Q(747^3) = 18 + 27 + 36 = 81 = 9^2.

Maple

isA153185 := proc(n) A007953(n)+A007953(n^2)+A007953(n^3) ; issqr(%) ; end proc:
for n from 1 to 2200 do if isA153185(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Jul 08 2010

Mathematica

sdnQ[n_]:=IntegerQ[Sqrt[Total[IntegerDigits[n]]+Total[IntegerDigits[ n^2]]+ Total[IntegerDigits[n^3]]]]; Select[Range[2100], sdnQ] (* Harvey P. Dale, Nov 25 2011 *)

Crossrefs

Sequence in context: A202187 A370016 A057373 * A325450 A212345 A086500

Adjacent sequences: A153182 A153183 A153184 * A153186 A153187 A153188

Keyword

easy,nonn,base

Author

Neven Juric (neven.juric(AT)apis-it.hr), Jul 07 2010, corrected Jul 09 2010

Extensions

1161 inserted by R. J. Mathar, Jul 08 2010

Status

approved