%I A126169
%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
%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 Pedersen J. M., <a href="http://amicable.homepage.dk/knwnc2.htm">Known 
               amicable pairs</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]}]
%Y A126169 Cf. A049417, A126168, A037445.
%Y A126169 Sequence in context: A160776 A043403 A122279 this_sequence A002952 A108344 
               A162675
%Y A126169 Adjacent sequences: A126166 A126167 A126168 this_sequence A126170 A126171 
               A126172
%K A126169 hard,nonn
%O A126169 1,1
%A A126169 Ant King (mathstutoring(AT)ntlworld.com), Dec 21 2006