A126161 Number of augmented amicable pairs (m,n) with m<n and for which m<=10^k, k=1,2,3,...

0, 0, 0, 1, 4, 9, 36, 84, 188, 420, 930, 1931

Offset

1,5

Links

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

J. M. Pedersen, Known amicable pairs.

Formula

An augmented amicable pair (m,n) is a pair of integers m, n with m<n and for which sigma(m)=sigma(n)=m+n-1

Example

a(6)=9 because there are 9 augmented amicable pairs with m<=10^6

Mathematica

s[n_]:=DivisorSigma[1, n]-n; AugmentedAmicableNumberQ[n_]:=If[s[s[n]+1]==n-1 && !DivisorSigma[1, n]==2n-1, True, False]; AugmentedAmicablePairList[ k_]:=(bnlist=Select[Range[k], AugmentedAmicableNumberQ[ # ]&]; newprlist= Table[Sort[{bnlist[[n]], s[bnlist[[n]]]+1}], {n, 1, Length[bnlist]}]; augamprlist=Union[newprlist, newprlist]); data=AugmentedAmicablePairList[10^7]; Table[Length[Select[data, First[ # ]<10^k &]], {k, 1, 7}]

Crossrefs

Cf. A007992, A015630.

Sequence in context: A115700 A029806 A133125 * A179934 A239213 A346537

Adjacent sequences: A126158 A126159 A126160 * A126162 A126163 A126164

Keyword

hard,nonn

Author

Ant King, Dec 20 2006

Status

approved