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 A386537 #7 Jul 25 2025 04:29:57
%S A386537 0,1,0,2,0,1,0,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,0,1,2,0,1,0,0,1,0,2,0,1,
%T A386537 0,0,1,0,2,0,1,0,4,0,1,0,2,0,0,0,1,0,2,0,1,0,0,1,0,2,0,1,0,0,1,0,2,0,
%U A386537 1,0,4,0,1,0,2,0,1,0,0,1,0,2,0,1,0,0,1
%N A386537 Exponent of the highest power of 2 dividing the n-th number whose prime factorization exponents are all powers of 2 (A138302).
%H A386537 Amiram Eldar, <a href="/A386537/b386537.txt">Table of n, a(n) for n = 1..10000</a>
%F A386537 a(n) = A007814(A138302(n)).
%F A386537 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (1 + Sum_{k>=0} (2^k + 1)/2^(2^k)) / (1 + Sum_{k>=0} 1/2^(2^k)) - 1 = 0.70550483007968767769... .
%t A386537 exp2nQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # == 2^IntegerExponent[#, 2] &];
%t A386537 IntegerExponent[Select[Range[200], exp2nQ], 2]
%o A386537 (PARI) isexp2n(n) = {my(f = factor(n)); for(i=1, #f~, if(f[i, 2] >> valuation(f[i, 2], 2) > 1, return (0))); 1;}
%o A386537 list(lim) = for(k = 1, lim, if(isexp2n(k), print1(valuation(k, 2), ", ")));
%Y A386537 Cf. A007404, A007814, A138302.
%Y A386537 Similar sequences: A383004, A383005, A383006, A383007, A383029, A383032, A386536.
%K A386537 nonn,easy
%O A386537 1,4
%A A386537 _Amiram Eldar_, Jul 25 2025