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Number of unitary amicable pairs (i,j) with i<j and i<=10^n.
0

%I #2 Mar 30 2012 18:41:04

%S 0,0,1,2,7,19,78,185,454,1095,2552,6105

%N Number of unitary amicable pairs (i,j) with i<j and i<=10^n.

%H Pedersen J. M., <a href="http://amicable.homepage.dk/knwnc2.htm">Known amicable pairs</a>.

%F The number of integer pairs (m,n) with m<n for which usigma(m)=usigma(n)=m+n.

%e a(7)=78 because there are 78 unitary amicable pairs with m<=10^7

%t UnitaryDivisors[n_Integer?Positive] := Select[Divisors[n], GCD[ #, n/# ] == 1 \ &]; sstar[n_] := Plus @@ UnitaryDivisors[ n] - n; UnitaryAmicableNumberQ[k_] := If[Nest[sstar, k, 2] == k && ! sstar[k] == k, True, False]; UnitaryAmicablePairList[ k_] := (anlist = Select[Range[k], UnitaryAmicableNumberQ[ # ] &]; prlist = \ Table[Sort[{anlist[[n]], sstar[anlist[[ n]]]}], {n, 1, Length[anlist]}]; data = Union[prlist, prlist]); UnitaryAmicablePairList[10^7]; Table[Length[Select[data, First[ # ] < \ 10^k &]], {k, 1, 7}]

%Y Cf. A034448.

%K hard,nonn

%O 1,4

%A _Ant King_, Dec 20 2006