1,1

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.

Pedersen J. M., Known amicable pairs.

The values of m for which isigma(m)=isigma(n)=m+n+1, where m<n and isigma(n) is given by A049417(n).

a(3)=573560 because 573560 is the smaller element of the third reduced infinitary amicable pair, (573560, 817479)

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]}]

Cf. A126169, A049417, A126168, A037445, A126170, A126171, A126173, A126174, A126175, A126176.

Sequence in context: A013687 A126821 A156855 this_sequence A031768 A156856 A031633

Adjacent sequences: A126169 A126170 A126171 this_sequence A126173 A126174 A126175

hard,nonn,more

Ant King (mathstutoring(AT)ntlworld.com), Dec 23 2006