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 A280543 #11 Feb 16 2025 08:33:39
%S A280543 1,1,2,4,8,16,31,62,123,244,483,958,1899,3765,7463,14794,29329,58141,
%T A280543 115258,228486,452949,897922,1780031,3528716,6995293,13867402,
%U A280543 27490602,54497104,108034531,214166610,424561814,841647229,1668473323,3307565365,6556885566,12998306479,25767716954,51081672682
%N A280543 Expansion of 1/(1 - x - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221).
%C A280543 Number of compositions (ordered partitions) of n into prime powers (1 included).
%H A280543 G. C. Greubel, <a href="/A280543/b280543.txt">Table of n, a(n) for n = 0..1000</a>
%H A280543 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%H A280543 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A280543 G.f.: 1/(1 - x - Sum_{k>=2} floor(1/omega(k))*x^k).
%e A280543 a(3) = 4 because we have [3], [2, 1], [1, 2] and [1, 1, 1].
%t A280543 nmax = 37; CoefficientList[Series[1/(1 - x - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
%Y A280543 Cf. A000961, A001221, A023893, A280195.
%K A280543 nonn
%O A280543 0,3
%A A280543 _Ilya Gutkovskiy_, Jan 05 2017