%I #24 Sep 08 2022 08:45:38

%S 1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,

%T 100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,

%U 10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100,1,10,100

%N Cubefree part of 10^n.

%C Period 3: repeat [1, 10, 100].

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

%F a(n) = 10^(n mod 3) = A050985(A011557(n)) = A011557(A010872(n)). - _Amiram Eldar_, Feb 14 2021

%F From _Wesley Ivan Hurt_, Apr 18 2021: (Start)

%F G.f.: (1+10*x+100*x^2)/(1-x^3).

%F a(n) = a(n-3). (End)

%t CubefreePart[n_Integer?Positive] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 3]} & /@ FactorInteger[n]); Table[CubefreePart[10^n], {n, 1, 40}]

%t PadRight[{}, 50, {1, 10, 100}] (* _Wesley Ivan Hurt_, Apr 18 2021 *)

%o (Magma) &cat [[1, 10,100]^^30]; // _Wesley Ivan Hurt_, Apr 18 2021

%Y Cf. A004709, A010872, A011557, A050985, A069705, A145642, A145643.

%K nonn,easy,less

%O 0,2

%A _Artur Jasinski_, Oct 15 2008

%E Offset corrected by _Amiram Eldar_, Feb 14 2021