

A126169


Smaller member of an infinitary amicable pair.


10



114, 594, 1140, 4320, 5940, 8640, 10744, 12285, 13500, 25728, 35712, 44772, 60858, 62100, 67095, 67158, 74784, 79296, 79650, 79750, 86400, 92960, 118500, 118944, 142310, 143808, 177750, 185368, 204512, 215712, 298188, 308220
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OFFSET

1,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..32.
Pedersen J. M., Known amicable pairs.


FORMULA

The values of m for which isigma(m)=isigma(n)=m+n and m<n


EXAMPLE

a(5)=5940 because the fifth infinitary amicable pair is (5940,8460) and 5940 is its smallest member


MATHEMATICA

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]}]


CROSSREFS

Cf. A049417, A126168, A037445.
Sequence in context: A122279 A251481 A251475 * A174072 A251459 A251452
Adjacent sequences: A126166 A126167 A126168 * A126170 A126171 A126172


KEYWORD

hard,nonn


AUTHOR

Ant King, Dec 21 2006


STATUS

approved



