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 A383004 #9 Apr 12 2025 09:42:24
%S A383004 0,1,0,2,0,1,0,0,1,0,2,0,1,0,0,1,0,2,0,1,0,0,1,2,0,1,0,0,1,0,2,0,1,0,
%T A383004 0,1,0,2,0,1,0,0,1,0,2,0,0,0,1,0,2,0,1,0,0,1,0,2,0,1,0,0,1,0,2,0,1,0,
%U A383004 1,0,2,0,1,0,0,1,0,2,0,1,0,0,1,0,2,0,1
%N A383004 Exponent of the highest power of 2 dividing the n-th cubefree number.
%H A383004 Amiram Eldar, <a href="/A383004/b383004.txt">Table of n, a(n) for n = 1..10000</a>
%F A383004 a(n) = A007814(A004709(n)).
%F A383004 A383009(a(n)) > 0.
%F A383004 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4/7.
%t A383004 cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; IntegerExponent[Select[Range[200], cubeFreeQ], 2]
%o A383004 (PARI) iscubefree(n) = {my(f = factor(n)); for(i=1, #f~, if(f[i, 2] > 2, return (0))); 1; }
%o A383004 list(lim) = for(k = 1, lim, if(iscubefree(k), print1(valuation(k, 2), ", ")));
%Y A383004 Cf. A004709, A007814, A373550, A383005, A383009.
%K A383004 nonn,easy
%O A383004 1,4
%A A383004 _Amiram Eldar_, Apr 12 2025