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 A334901 #11 May 17 2020 02:15:41
%S A334901 1,2,6,8,24,30,40,42,54,56,66,72,78,88,104,120,128,168,210,216,264,
%T A334901 270,280,312,330,360,378,384,390,408,440,456,462,480,504,510,520,546,
%U A334901 552,570,594,600,616,640,672,680,690,696,702,714,728,744,750,760,792,798
%N A334901 Infinitary practical numbers: numbers m such that every number 1 <= k <= isigma(m) is a sum of distinct infinitary divisors of m, where isigma is A049417.
%C A334901 Includes the powers of 2 of the form 2^(2^k - 1) for k = 0, 1, ... (A058891). The other terms are a subset of infinitary abundant numbers (A129656) and infinitary pseudoperfect numbers (A306983).
%H A334901 Amiram Eldar, <a href="/A334901/b334901.txt">Table of n, a(n) for n = 1..10000</a>
%t A334901 bin[n_] := 2^(-1 + Position[Reverse @ IntegerDigits[n, 2], _?(# == 1 &)] // Flatten); f[p_, e_] := p^bin[e]; icomp[n_] := Flatten[f @@@ FactorInteger[n]]; 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[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; infPracQ[n_] := Module[{f, p, e, prod = 1, ok = True}, If[n < 1 || (n > 1 && OddQ[n]), False, If[n == 1, True, r = Sort[icomp[n]]; Do[If[r[[i]] > 1 + isigma[prod], ok = False; Break[]]; prod = prod*r[[i]], {i, Length[r]}]; ok]]]; Select[Range[1000], infPracQ]
%Y A334901 The infinitary version of A005153.
%Y A334901 Cf. A049417, A058891, A129656, A286652, A306983, A334898.
%K A334901 nonn
%O A334901 1,2
%A A334901 _Amiram Eldar_, May 16 2020