Search: id:A126170
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%I A126170
%S A126170 126,846,1260,7920,8460,11760,10856,14595,17700,43632,45888,49308,
%T A126170 83142,62700,71145,73962,96576,83904,107550,88730,178800,112672,
%U A126170 131100,125856,168730,149952,196650,203432,206752,224928,306612
%N A126170 Larger member of an infinitary amicable pair.
%C A126170 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 A126170 Pedersen J. M., <a href="http://amicable.homepage.dk/knwnc2.htm">Known 
               amicable pairs</a>.
%F A126170 The values of n for which isigma(m)=isigma(n)=m+n and n>m.
%e A126170 a(5)=8460 because the fifth infinitary amicable pair is (5940,8460) and 
               8460 is its largest member
%t A126170 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[Last[data4[[k]]], 
               {k, 1, Length[data4]}]
%Y A126170 Cf. A126169, A049417, A126168, A037445.
%Y A126170 Sequence in context: A165023 A107658 A004008 this_sequence A151989 A104678 
               A154093
%Y A126170 Adjacent sequences: A126167 A126168 A126169 this_sequence A126171 A126172 
               A126173
%K A126170 hard,nonn
%O A126170 1,1
%A A126170 Ant King (mathstutoring(AT)ntlworld.com), Dec 21 2006

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