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 A126169 #11 Jan 24 2019 03:42:23
%S A126169 114,594,1140,4320,5940,8640,10744,12285,13500,25728,35712,44772,
%T A126169 60858,62100,67095,67158,74784,79296,79650,79750,86400,92960,118500,
%U A126169 118944,142310,143808,177750,185368,204512,215712,298188,308220,356408,377784,420640,462330
%N A126169 Smaller member of an infinitary amicable pair.
%C A126169 A divisor of n is called infinitary if it is a product of divisors of the form p^{y_a 2^a}, where p^y is a prime power dividing n and sum_a y_a 2^a is the binary representation of y.
%H A126169 Amiram Eldar, <a href="/A126169/b126169.txt">Table of n, a(n) for n = 1..7916</a>
%H A126169 Jan Munch Pedersen, <a href="http://62.198.248.44/aliquot/tables.htm">Tables of Aliquot Cycles</a>.
%F A126169 The values of m for which isigma(m)=isigma(n)=m+n and m<n.
%e A126169 a(5)=5940 because the fifth infinitary amicable pair is (5940,8460) and 5940 is its smallest member
%t A126169 ExponentList[n_Integer, factors_List] := {#, IntegerExponent[n, # ]} & /@ factors; InfinitaryDivisors[1] := {1}; InfinitaryDivisors[n_Integer?Positive] := Module[ { factors = First /@ FactorInteger[n], d = Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f, g}, BitOr[f, g] == g][ #, Last[ # ]]] & /@ Transpose[Last /@ ExponentList[ #, factors] & /@ d]], _?( And @@ # &), {1}]] ]] ] Null; properinfinitarydivisorsum[k_] := Plus @@ InfinitaryDivisors[k] - k; InfinitaryAmicableNumberQ[k_] := If[Nest[properinfinitarydivisorsum, k, 2] == k && ! properinfinitarydivisorsum[k] == k, True, False]; data1 = Select[ Range[10^6], InfinitaryAmicableNumberQ[ # ] &]; data2 = properinfinitarydivisorsum[ # ] & /@ data1; data3 = Table[{data1[[k]], data2[[k]]}, {k, 1, Length[data1]}]; data4 = Select[data3, First[ # ] < Last[ # ] &]; Table[First[data4[[k]]], {k, 1, Length[data4]}]
%t A126169 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}]]; infs[n_] := Times @@ (fun @@@ FactorInteger[n]) - n; s = {}; Do[k = infs[n]; If[k > n && infs[k] == n, AppendTo[s, n]], {n, 2, 10^5}]; s (* _Amiram Eldar_, Jan 22 2019 *)
%Y A126169 Cf. A049417, A126168, A037445.
%K A126169 nonn
%O A126169 1,1
%A A126169 _Ant King_, Dec 21 2006
%E A126169 a(33)-a(36) from _Amiram Eldar_, Jan 22 2019