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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.
0
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
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
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