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 A383007 #8 Apr 12 2025 09:41:53
%S A383007 0,3,4,0,5,6,0,0,7,3,0,8,0,4,9,0,3,0,5,3,10,4,0,6,3,4,11,0,0,0,5,3,0,
%T A383007 0,7,4,5,12,0,3,6,4,3,0,0,8,5,6,13,0,4,0,7,3,5,4,0,9,0,6,0,7,14,0,0,3,
%U A383007 3,3,0,5,8,4,6,5,0,3,3,10,0,0,0,0,7,8,15
%N A383007 Exponent of the highest power of 2 dividing the n-th cubefull number.
%H A383007 Amiram Eldar, <a href="/A383007/b383007.txt">Table of n, a(n) for n = 1..10000</a>
%H A383007 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A383007 a(n) = A007814(A036966(n)).
%F A383007 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 + 2^(1/3) + 2^(2/3) = 4.847322... .
%t A383007 IntegerExponent[Select[Range[100000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 2 &], 2]
%o A383007 (PARI) iscubefull(k) = if(k == 1, 1, my(e = factor(k)[, 2]); vecmin(e) > 2);
%o A383007 list(lim) = for(k = 1, lim, if(iscubefull(k), print1(valuation(k, 2), ", ")));
%Y A383007 Cf. A007814, A036966, A383006.
%K A383007 nonn,easy
%O A383007 1,2
%A A383007 _Amiram Eldar_, Apr 12 2025