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A113768 a(1) = 1, a(n+1) = a(n) + floor(a(n)^(1/3)).

%I A113768 #28 Feb 14 2024 15:06:17
%S A113768 1,2,3,4,5,6,7,8,10,12,14,16,18,20,22,24,26,28,31,34,37,40,43,46,49,
%T A113768 52,55,58,61,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,
%U A113768 128,133,138,143,148,153,158,163,168,173,178,183,188,193,198,203,208,213,218,224,230,236,242,248,254,260
%N A113768 a(1) = 1, a(n+1) = a(n) + floor(a(n)^(1/3)).
%C A113768 First 17 terms identical to A079645 (Integer part of the cube root of n divides n). Replacing cube root by square root gives A033638.
%H A113768 Robert Israel, <a href="/A113768/b113768.txt">Table of n, a(n) for n = 1..10000</a>
%F A113768 Conjecture: a(n) ~ (2/3)*n*sqrt((2/3)*n). - _José María Grau Ribas_, Feb 13 2024
%p A113768 A[1]:= 1:
%p A113768 for n from 1 to 100 do A[n+1] := A[n] + floor(A[n]^(1/3)) od:
%p A113768 seq(A[i],i=1..100); # _Robert Israel_, Jul 28 2019
%t A113768 NestList[#+Floor[Surd[#,+3]]&,1,70] (* _Harvey P. Dale_, Jan 21 2013 *)
%o A113768 (Magma) [n le 1 select 1 else Self(n-1)+Floor(Self(n-1)^(1/3)): n in [1..75]]; // _Vincenzo Librandi_, Jul 29 2019
%Y A113768 Cf. A033638, A048766, A079645.
%K A113768 nonn,easy
%O A113768 1,2
%A A113768 _Jonathan Vos Post_, Jan 19 2006
%E A113768 Corrected and extended by _Harvey P. Dale_, Jan 21 2013