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 A282500 #7 Feb 16 2025 08:33:41
%S A282500 1,1,1,1,2,3,4,5,8,13,19,26,37,55,81,116,167,244,358,520,752,1091,
%T A282500 1589,2311,3354,4870,7081,10298,14963,21734,31580,45900,66704,96919,
%U A282500 140827,204654,297413,432180,627996,912565,1326117,1927054,2800260,4069160,5913116,8592675,12486402,18144506,26366614
%N A282500 Expansion of 1/(1 - Sum_{k = i^j, i>=1, j>=2} x^k).
%C A282500 Number of compositions (ordered partitions) into perfect powers (A001597).
%H A282500 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">Perfect Powers</a>
%H A282500 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A282500 G.f.: 1/(1 - Sum_{k = i^j, i>=1, j>=2} x^k).
%F A282500 a(n) ~ c / r^n, where r = 0.68816189979082638501485812136220175833447947220530020978433949588627... and c = 0.4267808681995359684192168334905096310027880655306734537865362460298... . - _Vaclav Kotesovec_, Feb 17 2017
%e A282500 a(7) = 5 because we have [4, 1, 1, 1], [1, 4, 1, 1], [1, 1, 4, 1], [1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1].
%t A282500 nmax = 95; CoefficientList[Series[1/ (1 - x - Sum[Boole[GCD @@ FactorInteger[k][[All, 2]] > 1] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
%Y A282500 Cf. A001597, A078635, A112344.
%K A282500 nonn
%O A282500 0,5
%A A282500 _Ilya Gutkovskiy_, Feb 16 2017