This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A076936 #26 Mar 20 2024 16:19:31
%S A076936 1,4,2,32,4,256,8,2048,16,16384,32,131072,64,1048576,128,8388608,256,
%T A076936 67108864,512,536870912,1024,4294967296,2048,34359738368,4096,
%U A076936 274877906944,8192,2199023255552,16384,17592186044416,32768
%N A076936 a(1) = 1; then the smallest number different from its predecessor such that the n-th partial product is an n-th power.
%C A076936 Or "such that the geometric mean of the first n terms is an integer." (Without the "different from its predecessor" requirement, the trivial sequence 1,4,2,2,2,2,2,... would have resulted.)
%H A076936 Robert Israel, <a href="/A076936/b076936.txt">Table of n, a(n) for n = 1..2209</a>
%H A076936 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 10, 0, -16).
%F A076936 From _Robert Israel_, Nov 27 2016: (Start)
%F A076936 a(n) = 2^A014682(n-1).
%F A076936 G.f.: x*(1+4*x-8*x^2-8*x^3)/(1-10*x^2+16*x^4). (End)
%p A076936 seq(op([2^k,2^(3*k+2)]),k=0..20); # _Robert Israel_, Nov 27 2016
%t A076936 CoefficientList[Series[x (1 + 4 x - 8 x^2 - 8 x^3)/(1 - 10 x^2 + 16 x^4), {x, 0, 31}], x] (* _Michael De Vlieger_, Nov 24 2017 *)
%t A076936 LinearRecurrence[{0,10,0,-16},{1,4,2,32},40] (* _Harvey P. Dale_, Mar 20 2024 *)
%Y A076936 Cf. A014682, A016116.
%K A076936 nonn
%O A076936 1,2
%A A076936 _Amarnath Murthy_, Oct 19 2002
%E A076936 More terms from _Sam Alexander_, Nov 15 2003