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%I #13 Feb 26 2019 05:03:53
%S 9,18,45,90,171,180,207,279,297,396,414,450,459,486,567,576,693,702,
%T 729,738,747,900,918,954,981,1062,1134,1161,1197,1206,1215,1233,1323,
%U 1332,1341,1431,1449,1467,1485,1494,1503,1656,1710,1737,1755,1800,1908,2007
%N 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.
%H Pedro Henrique O. Pantoja, <a href="https://cms.math.ca/crux/v36/n1/Problems_36_1.pdf">Problem 3506</a>, Crux Mathematicorum, February 2010, Volume 36 Number 1, p. 45.
%e 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.
%p isA153185 := proc(n) A007953(n)+A007953(n^2)+A007953(n^3) ; issqr(%) ; end proc:
%p for n from 1 to 2200 do if isA153185(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Jul 08 2010
%t 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 *)
%K easy,nonn,base
%O 1,1
%A Neven Juric (neven.juric(AT)apis-it.hr), Jul 07 2010, corrected Jul 09 2010
%E 1161 inserted by _R. J. Mathar_, Jul 08 2010
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