A126162 Number of unitary amicable pairs (i,j) with i<j and i<=10^n.

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

Offset

1,4

Links

Table of n, a(n) for n=1..12.

Pedersen J. M., Known amicable pairs.

Formula

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

Example

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

Mathematica

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}]

Crossrefs

Cf. A034448.

Sequence in context: A243279 A362097 A080873 * A054423 A137990 A056650

Adjacent sequences: A126159 A126160 A126161 * A126163 A126164 A126165

Keyword

hard,nonn

Author

Ant King, Dec 20 2006

Status

approved