A126163 Number of super unitary amicable pairs (i,j) with i<j and i<=10^n.

0, 1, 8, 27, 102, 375, 1134, 3589, 11942, 40410

Offset

1,3

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Super unitary amicable pairs

Formula

Integer pairs (m,n) with m<n and for which usigma(usigma(m))=usigma(usigma(n))=m+n.

Example

a(6)=375 because there are 375 super unitary (m,n) pairs with m<n and for which m<=10^6

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}]

Crossrefs

Cf. A045613, A045614.

Sequence in context: A079712 A056598 A343283 * A307117 A331285 A183316

Adjacent sequences: A126160 A126161 A126162 * A126164 A126165 A126166

Keyword

hard,nonn,more

Author

Ant King, Dec 20 2006

Extensions

a(8)-a(10) from Amiram Eldar, Feb 18 2019

Status

approved