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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 22 00:41 EST 2014. Contains 252326 sequences.