A117676 Squares for which the digital root is also a square.

0, 1, 4, 9, 36, 49, 64, 81, 100, 121, 144, 225, 256, 289, 324, 361, 400, 441, 576, 625, 676, 729, 784, 841, 900, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3600, 3721, 3844

Offset: 0

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 12 2006

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290.

Programs

Mathematica

drQ[n_]:=IntegerQ[Sqrt[NestWhile[Total[IntegerDigits[#]]&,n,#>9&]]]; Select[Range[0,100]^2,drQ] (* Harvey P. Dale, Feb 14 2016 *)

Formula

Empirical g.f.: -x*(x +1)*(x^12 +2*x^11 +3*x^10 +24*x^9 -11*x^8 +26*x^7 -9*x^6 +26*x^5 -11*x^4 +24*x^3 +3*x^2 +2*x +1) / ((x -1)^3*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)^2). - Colin Barker, Jan 17 2014