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%I #10 Apr 10 2023 06:50:06
%S 2394,7544,10184,1452330,2154584,5021912,5747994,5771934,5786298,
%T 5800662,5834178,5843754,5858118,5886846,5905998,5920362,5929938,
%U 5992182,6035274,6059214,6078366,6087942,6102306,6107094,6121458,6174126,6202854,6207642,6245946,6265098
%N Numbers k whose infinitary divisors have an even sum which is larger than 2k, but they cannot be partitioned into two disjoint parts whose sums are equal.
%C The infinitary version of A171641.
%H Amiram Eldar, <a href="/A323344/b323344.txt">Table of n, a(n) for n = 1..10000</a>
%t infdivs[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]] ; fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[n_] := If[n == 1, 1, Times @@ (fun @@@ FactorInteger[n])]; seq={}; Do[s=isigma[n]; If[OddQ[s] || s<=2n, Continue[]]; div = infdivs[n]; If[Coefficient[Times @@ (1 + x^div) // Expand, x, s/2] == 0, AppendTo[seq, n]], {n, 1, 100000}]; seq (* after _Michael De Vlieger_ at A077609 *)
%Y Cf. A049417, A077609, A129656, A171641, A323341, A323342, A323343.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jan 11 2019
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