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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Pedro Henrique O. Pantoja, Crux Problem 3506.

LINKS

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

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

Contribution from R. J. Mathar, Jul 08 2010: (Start)

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: (End)

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: A138900 A202187 A057373 * A212345 A086500 A022669

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

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Last modified June 28 09:49 EDT 2017. Contains 288813 sequences.