A118468 Numbers n for which the sum of the digits plus the sum of the digits of the square, equals the sum of the digits of the cube.

0, 9, 18, 27, 36, 45, 54, 72, 90, 99, 108, 135, 162, 180, 189, 198, 216, 225, 243, 270, 288, 306, 315, 333, 360, 405, 432, 441, 450, 495, 504, 513, 522, 531, 540, 594, 603, 612, 621, 639, 648, 657, 666, 675, 720, 765, 783, 801, 819, 837, 846, 855, 873, 882

Offset

1,2

Comments

s(n) stands for the sum of the digits of n.

Links

Table of n, a(n) for n=1..54.

Formula

s(n)+s(n^2)=s(n^3)

Example

45 is in the sequence because (1) the sum of the digits is 4+5=9, (2) the sum of the digits of 45^2 = 2025 is 2+0+2+5=9, (3) the sum of the digits of 45^3=91125 is 9+1+1+2+5=18 and (4) 9+9=18

Mathematica

dgsQ[n_]:=Total[IntegerDigits[n]]+Total[IntegerDigits[n^2]]== Total[ IntegerDigits[ n^3]]; Select[Range[0, 900], dgsQ] (* Harvey P. Dale, Aug 02 2011 *)

Crossrefs

Sequence in context: A044834 A033006 A259727 * A206905 A083497 A067552

Adjacent sequences: A118465 A118466 A118467 * A118469 A118470 A118471

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), May 04 2006

Status

approved