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 A383005 #7 Apr 12 2025 09:41:35
%S A383005 0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,0,1,0,2,
%T A383005 0,1,0,3,0,1,0,2,0,1,0,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,0,1,0,2,0,1,0,3,
%U A383005 0,1,0,2,0,1,0,1,0,2,0,1,0,3,0,1,0,2,0
%N A383005 Exponent of the highest power of 2 dividing the n-th biquadratefree number.
%C A383005 First differs from A254990 at n = 31.
%H A383005 Amiram Eldar, <a href="/A383005/b383005.txt">Table of n, a(n) for n = 1..10000</a>
%F A383005 a(n) = A007814(A046100(n)).
%F A383005 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 11/15.
%F A383005 In general, the asymptotic mean of the exponent of the highest power of 2 dividing the n-th k-free number (number that is not divisible by a k-th power other than 1), for k >= 2, is 1 - k/(2^k-1).
%t A383005 biqFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 4 &]; IntegerExponent[Select[Range[200], biqFreeQ], 2]
%o A383005 (PARI) isbiqfree(n) = {my(f = factor(n)); for(i=1, #f~, if(f[i, 2] > 3, return (0))); 1; }
%o A383005 list(lim) = for(k = 1, lim, if(isbiqfree(k), print1(valuation(k, 2), ", ")));
%Y A383005 Cf. A046100, A007814, A254990, A373550, A383004.
%K A383005 nonn,easy
%O A383005 1,4
%A A383005 _Amiram Eldar_, Apr 12 2025