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 A317946 #15 Jan 21 2024 02:24:02
%S A317946 0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,3,0,1,0,1,0,0,0,1,1,0,1,1,0,0,0,3,0,0,
%T A317946 0,2,0,0,0,1,0,0,0,1,1,0,0,3,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,4,0,0,0,1,
%U A317946 0,0,0,2,0,0,1,1,0,0,0,3,3,0,0,1,0,0,0,1,0,1,0,1,0,0,0,3,0,1,1,2,0,0,0,1,0
%N A317946 Additive with a(p^e) = A011371(e); the 2-adic valuation of A317934(n).
%C A317946 Records are A005187, occurring at A000302 (powers of 4).
%H A317946 Antti Karttunen, <a href="/A317946/b317946.txt">Table of n, a(n) for n = 1..65537</a>
%F A317946 a(n) = A007814(A317934(n)).
%F A317946 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime, k>=1} 1/(p^(2^k) - 1) = 0.63710219855356676263... . - _Amiram Eldar_, Jan 21 2024
%t A317946 f[p_, e_] := e - DigitCount[e, 2, 1]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 21 2024 *)
%o A317946 (PARI)
%o A317946 A011371(n) = (n - hammingweight(n));
%o A317946 A317934(n) = vecsum(apply(e -> A011371(e),factor(n)[,2]));
%Y A317946 Cf. A000302, A005187, A011371, A317934.
%Y A317946 Cf. also A046645.
%K A317946 nonn
%O A317946 1,16
%A A317946 _Antti Karttunen_, Aug 24 2018