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 A323343 #10 Apr 10 2023 06:50:15
%S A323343 1910412,9552060,21014532,24835356,32477004,43939476,55401948,
%T A323343 59222772,70685244,78326892,82147716,89789364,101251836,105072660,
%U A323343 112714308,116535132,124176780,127997604,135639252,139460076,150922548,158564196,162385020,170026668,185309964
%N A323343 Numbers k whose exponential divisors have an even sum which is larger than 2k, but they cannot be partitioned into two disjoint parts whose sums are equal.
%C A323343 The exponential version of A171641.
%H A323343 Amiram Eldar, <a href="/A323343/b323343.txt">Table of n, a(n) for n = 1..1000</a>
%t A323343 dQ[n_, m_] := (n>0&&m>0 &&Divisible[n, m]); expDivQ[n_, d_] := Module[ {ft = FactorInteger[n]}, And@@MapThread[dQ, {ft[[;; , 2]], IntegerExponent[ d, ft[[;; , 1]]]} ]]; ediv[n_] := Module[ {d=Rest[Divisors[n]]}, Select[ d, expDivQ[n, #]&]]; esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[ Last[#]]}] &) /@ FactorInteger[n]; seq={}; Do[s=esigma[n]; If[OddQ[s] || s<=2n, Continue[]]; div = ediv[n]; If[Coefficient[Times @@ (1 + x^div) // Expand, x, s/2] == 0, AppendTo[seq, n]], {n, 1, 10000}]; seq
%Y A323343 Cf. A051377, A129575, A171641, A323341, A323342, A323344.
%K A323343 nonn
%O A323343 1,1
%A A323343 _Amiram Eldar_, Jan 11 2019