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 A370078 #9 May 24 2024 18:03:53
%S A370078 0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,2,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,
%T A370078 0,2,0,0,0,0,0,0,0,1,1,0,0,2,1,1,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,
%U A370078 0,0,0,1,0,0,1,1,0,0,0,2,2,0,0,1,0,0,0
%N A370078 a(n) = log_2(A370077(n)).
%H A370078 Amiram Eldar, <a href="/A370078/b370078.txt">Table of n, a(n) for n = 1..10000</a>
%F A370078 a(n) = A007814(A005361(A367168(n))).
%F A370078 Additive with a(p^e) = log_2(e) if e is a power of 2, and 0 otherwise.
%F A370078 a(n) = 0 if and only if n is an exponentially odd number (A268335).
%F A370078 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} k * (P(2^k)-P(2^k+1)) = 0.36616241880640645934..., where P(s) is the prime zeta function .
%t A370078 f[p_, e_] := If[e == 2^(k = IntegerExponent[e, 2]), k, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A370078 (PARI) s(n) = my(e = valuation(n, 2)); if(n >> e == 1, e, 0);
%o A370078 a(n) = vecsum(apply(x -> s(x), factor(n)[, 2]));
%Y A370078 Cf. A005361, A007814, A268335, A367168, A370077.
%K A370078 nonn,easy
%O A370078 1,16
%A A370078 _Amiram Eldar_, Feb 09 2024