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 A309843 #38 Sep 14 2019 06:36:47
%S A309843 24,360,4320,14688,1468800,9547200,50585472,54198720,189695520,
%T A309843 1680459264
%N A309843 Numbers m that equal the sum of their first k consecutive aliquot infinitary divisors, but not all of them (i.e k < A037445(m) - 1).
%C A309843 The infinitary version of Erdős-Nicolas numbers (A194472).
%C A309843 If all the aliquot infinitary divisors are permitted (i.e. k <= A037445(n) - 1), then the infinitary perfect numbers (A007357) are included.
%e A309843 24 is in the sequence since its aliquot infinitary divisors are 1, 2, 3, 4, 6, 8, 12 and 24 and 1 + 2 + 3 + 4 + 6 + 8 = 24.
%t A309843 idivs[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[ x ] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[idivs[n], -2]]; s= {}; Do[If[selDivs[n] == 0, AppendTo[s, n]], {n, 2, 10^6}]; s(* after _Alonso del Arte_ at A194472 *)
%Y A309843 Cf. A007357, A077609, A037445, A049417, A194472, A293618.
%K A309843 nonn,more
%O A309843 1,1
%A A309843 _Amiram Eldar_, Sep 14 2019