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 A126172 #10 Jan 22 2019 08:23:10
%S A126172 2024,62744,573560,1000824,1173704,1208504,1921185,2140215,2198504,
%T A126172 2312024,2580864,4012184,5416280,9247095,12500865,13496840,23939685,
%U A126172 26409320,34093304,37324584,40818855,52026920,66275384,76011992,79842104,101366342,101589320,106004024
%N A126172 Smaller element of a reduced infinitary amicable pair.
%C A126172 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 A126172 Amiram Eldar, <a href="/A126172/b126172.txt">Table of n, a(n) for n = 1..278</a>
%H A126172 Jan Munch Pedersen, <a href="http://62.198.248.44/aliquot/tables.htm">Tables of Aliquot Cycles</a>.
%F A126172 The values of m for which isigma(m)=isigma(n)=m+n+1, where m<n and isigma(n) is given by A049417(n).
%e A126172 a(3)=573560 because 573560 is the smaller element of the third reduced infinitary amicable pair, (573560, 817479)
%t A126172 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; ReducedInfinitaryAmicableNumberQ[n_] := If[properinfinitarydivisorsum[properinfinitarydivisorsum[ n] - 1] == n + 1 && n > 1, True, False]; ReducedInfinitaryAmicablePairList[k_] := (anlist = Select[Range[k], ReducedInfinitaryAmicableNumberQ[ # ] &]; prlist = Table[Sort[{anlist[[n]], properinfinitarydivisorsum[anlist[[n]]] - 1}], {n, 1, Length[anlist]}]; amprlist = Union[prlist, prlist]); data1 = ReducedInfinitaryAmicablePairList[ 10^7]; Table[First[data1[[k]]], {k, 1, Length[data1]}]
%t A126172 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] - 1; If[k > n && infs[k] == n + 1, AppendTo[s, n]], {n, 2, 10^5}]; s (* _Amiram Eldar_, Jan 22 2019 *)
%Y A126172 Cf. A126169, A049417, A126168, A037445, A126170, A126171, A126173, A126174, A126175, A126176.
%K A126172 nonn
%O A126172 1,1
%A A126172 _Ant King_, Dec 23 2006
%E A126172 a(15)-a(28) from _Amiram Eldar_, Jan 22 2019