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 A369934 #12 Mar 29 2025 03:26:47
%S A369934 0,0,1,0,0,0,1,0,0,1,0,0,0,2,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,0,
%T A369934 0,0,0,1,1,0,0,2,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,1,1,0,0,
%U A369934 0,2,2,0,0,1,0,0,0,0,1,0,1,0,0,0,0,1,1
%N A369934 a(n) = log_2(A369933(n)).
%H A369934 Amiram Eldar, <a href="/A369934/b369934.txt">Table of n, a(n) for n = 2..10001</a>
%F A369934 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=2..m} a(k) = (Sum_{k>=1} (k * (d(k) - d(k-1)))) / A271727 = 0.35202853155774942465..., where d(k) = Product_{p prime} (1 - 1/p^3 + Sum_{i=2..k} (1/p^(2^i)-1/p^(2^i+1))) for k >= 1, and d(0) = 1/zeta(2).
%t A369934 pow2Q[n_] := n == 2^IntegerExponent[n, 2]; f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[AllTrue[e, pow2Q], Log2[Max @@ e], Nothing]]; Array[f, 150, 2]
%o A369934 (PARI) ispow2(n) = n >> valuation(n, 2) == 1;
%o A369934 lista(kmax) = {my(e); for(k = 2, kmax, e = factor(k)[, 2]; if(ispow2(vecprod(e)), print1(logint(vecmax(e), 2), ", "))); }
%Y A369934 Cf. A013661, A271727, A369933.
%K A369934 nonn,easy
%O A369934 2,14
%A A369934 _Amiram Eldar_, Feb 06 2024