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 A383009 #7 Apr 12 2025 09:42:13
%S A383009 2,4,6,9,11,13,16,18,20,23,24,26,29,31,33,36,38,40,43,45,49,51,53,56,
%T A383009 58,60,63,65,67,69,71,73,76,78,80,83,85,87,90,93,96,98,100,103,105,
%U A383009 106,109,111,113,115,117,119,122,124,126,129,131,133,137,139,142,144
%N A383009 Indices of the even terms in the sequence of cubefree numbers.
%C A383009 The asymptotic density of this sequence is 3/7.
%C A383009 In general, the asymptotic density of the indices of the even terms in the sequence of k-free numbers (numbers that are not divisible by a k-th power other than 1), for k >= 2, is (2^(k-1)-1)/(2^k-1).
%H A383009 Amiram Eldar, <a href="/A383009/b383009.txt">Table of n, a(n) for n = 1..10000</a>
%F A383009 A383004(a(n)) > 0.
%t A383009 cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; Position[Select[Range[250], cubeFreeQ], _?EvenQ] // Flatten
%o A383009 (PARI) iscubefree(n) = {my(f = factor(n)); for(i=1, #f~, if(f[i, 2] > 2, return (0))); 1; }
%o A383009 list(lim) = {my(c = 0); for(k = 1, lim, if(iscubefree(k), c++; if(!(k % 2), print1(c, ", ")))); }
%Y A383009 Cf. A004709, A381822, A383004, A383008.
%K A383009 nonn,easy
%O A383009 1,1
%A A383009 _Amiram Eldar_, Apr 12 2025