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 A339916 #30 Dec 04 2023 04:49:25
%S A339916 1,3,5,9,19,33,65,135,257,513,1035,2049,4101,8211,16385,32769,65571,
%T A339916 131085,262145,524355,1048577,2097153,4194455,8388609,16777225,
%U A339916 33554691,67108865,134217765,268435971,536870913,1073741825,2147484699,4294967365,8589934593,17179871235,34359738369,68719476737
%N A339916 The sum of 2^((d-1)/2) over all divisors of 2n+1.
%C A339916 This is sort of a bitmap representation of the divisors of odd numbers.
%H A339916 Robert Israel, <a href="/A339916/b339916.txt">Table of n, a(n) for n = 0..3318</a>
%e A339916 For n=7, a(7)=2^7+2^2+2^1+2^0=135 because the divisors of 15 are 15,5,3,1.
%p A339916 seq(add(2^((d-1)/2),d=numtheory:-divisors(2*n+1)),n=0..100); # _Robert Israel_, Dec 24 2020
%t A339916 A339916[n_]:=Block[{d=Divisors[2n+1]},Sum[2^((d[[k]]-1)/2),{k,Length[d]}]];Array[A339916,50,0]
%o A339916 (PARI) a(n) = sumdiv(2*n+1, d, 2^((d-1)/2)); \\ _Michel Marcus_, Dec 23 2020
%o A339916 (Python)
%o A339916 from sympy import divisors
%o A339916 def a(n): return sum(2**((d-1)//2) for d in divisors(2*n+1))
%o A339916 print([a(n) for n in range(37)]) # _Michael S. Branicky_, Dec 24 2020
%Y A339916 Cf. A114001 (bit reversal), A034729, A055895.
%K A339916 nonn
%O A339916 0,2
%A A339916 _Don Knuth_, Dec 22 2020