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 A240951 #24 May 04 2023 06:33:01
%S A240951 1,2,5,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T A240951 131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U A240951 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592
%N A240951 Maximum number of dividing subsets of a set of n natural numbers.
%C A240951 Let A be a set of positive integers and B a subset of A. B is said to divide A if the sum of elements in B divides the sum of elements in A.
%H A240951 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F A240951 a(n) = 2^(n-1) = A000079(n-1) if n>4.
%F A240951 From _Stefano Spezia_, May 03 2023: (Start)
%F A240951 O.g.f.: x*(1 + x^2 - 2*x^3)/(1 - 2*x).
%F A240951 E.g.f.: (x^3 + 3*exp(2*x) - 3)/6. (End)
%e A240951 n = 3: only A={k,2k,3k}, where k is a natural number, has 5 dividing subsets.
%e A240951 n = 4: {1, 2, 3, 6} has 8 dividing subsets: {1}, {2}, {3}, {6}, {1, 2}, {1, 3}, {1, 2, 3}, {1, 2, 3, 6}. (Corrected by _Stan Wagon_, Nov 07 2015)
%t A240951 Join[{1,2,5},NestList[2#&,8,40]] (* _Harvey P. Dale_, Sep 19 2021 *)
%o A240951 (PARI) a(n)=if(n==3,5,2^(n-1)) \\ _Charles R Greathouse IV_, Nov 06 2015
%Y A240951 Cf. A000079.
%K A240951 nonn,easy
%O A240951 1,2
%A A240951 _Sebastian Raba_, Aug 04 2014