A126163
Number of super unitary amicable pairs (i,j) with i
0, 1, 8, 27, 102, 375, 1134, 3589, 11942, 40410
Offset: 1
Examples
a(6)=375 because there are 375 super unitary (m,n) pairs with m<n and for which m<=10^6
Links
- Eric Weisstein's World of Mathematics, Super unitary amicable pairs
Programs
-
Mathematica
UnitaryDivisors[n_Integer?Positive] := Select[Divisors[n], GCD[ #, n/# ] == 1 \ &]; UnitaryDivisorSum[n_Integer?Positive] := Plus @@ UnitaryDivisors[n]; f[ k_] := Nest[UnitaryDivisorSum, k, 2] - k; g[ k_] := Nest[UnitaryDivisorSum, f[k], 2] - f[k]; m = 10^7; data1 = Select[Range[m], g[ # ] == # &]; data2 = Nest[UnitaryDivisorSum, #, 2] - # & /@ data1; data3 = Table[{data1[[k]], data2[[k]]}, {k, 1, Length[data1]}]; data4 = DeleteCases[Table[If[Nest[UnitaryDivisorSum, First[data3[[k]]], 2] == Nest[UnitaryDivisorSum, Last[data3[[k]]], 2] \ && ! First[data3[[k]]] >= Last[data3[[k]]], data3[[k]], 0], {k, 1, Length[data3]}], 0]; data5 = Table[Length[Select[data4, First[ # ] < 10^k \ &]], {k, 1, 7}]