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 A385047 #8 Jun 16 2025 16:53:00
%S A385047 1,3,1,5,1,3,1,9,1,3,1,5,1,3,1,17,1,3,1,5,1,3,1,9,1,3,1,5,1,3,1,33,1,
%T A385047 3,1,5,1,3,1,9,1,3,1,5,1,3,1,17,1,3,1,5,1,3,1,9,1,3,1,5,1,3,1,65,1,3,
%U A385047 1,5,1,3,1,9,1,3,1,5,1,3,1,17,1,3,1,5,1,3
%N A385047 The sum of the unitary divisors of n that are powers of 2.
%H A385047 Amiram Eldar, <a href="/A385047/b385047.txt">Table of n, a(n) for n = 1..10000</a>
%F A385047 Multiplicative with a(2^e) = 2^e + 1, and a(p^e) = 1 for an odd prime p.
%F A385047 a(n) = A034448(n) / A192066(n).
%F A385047 a(n) = A059841(n) + A006519(n), i.e., a(n) = A006519(n) + 1 if n is even, and 1 is n is odd.
%F A385047 Dirichlet g.f.: zeta(s) * ((1-1/2^(2*s-1))/(1-1/2^(s-1))).
%F A385047 Sum_{k=1..n} a(k) ~ (n/(2*log(2))) * (log(n) + gamma - 1 + 5*log(2)/2), where gamma is Euler's constant (A001620).
%t A385047 a[n_] := If[OddQ[n], 1, 2^IntegerExponent[n, 2] + 1]; Array[a, 100]
%o A385047 (PARI) a(n) = if(n%2, 1, 2^valuation(n, 2)+1);
%Y A385047 The unitary analog of A038712.
%Y A385047 Cf. A001620, A006519, A034448.
%Y A385047 The sum of unitary divisors of n that are: A092261 (squarefree), A192066 (odd), A358346 (exponentially odd), A358347 (square), A360720 (powerful), A371242 (cubefree), A380396 (cube), A383763 (exponentially squarefree), A385043 (exponentially 2^n), A385045 (5-rough), A385046 (3-smooth), this sequence (power of 2), A385048 (cubefull), A385049 (biquadratefree).
%K A385047 nonn,easy,mult
%O A385047 1,2
%A A385047 _Amiram Eldar_, Jun 16 2025