A126161
Number of augmented amicable pairs (m,n) with m
0, 0, 0, 1, 4, 9, 36, 84, 188, 420, 930, 1931
Offset: 1
Examples
a(6)=9 because there are 9 augmented amicable pairs with m<=10^6
Links
- Shyam Sunder Gupta, Amicable Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 5, 159-183.
- Jan Munch Pedersen, Known amicable pairs.
Programs
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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}]
Formula
An augmented amicable pair (m,n) is a pair of integers m, n with m