This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A126161 #7 Mar 11 2025 08:43:18
%S A126161 0,0,0,1,4,9,36,84,188,420,930,1931
%N A126161 Number of augmented amicable pairs (m,n) with m<n and for which m<=10^k, k=1,2,3,...
%H A126161 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_5">Amicable Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 5, 159-183.
%H A126161 Jan Munch Pedersen, <a href="http://amicable.homepage.dk/knwnc2.htm">Known amicable pairs</a>.
%F A126161 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
%e A126161 a(6)=9 because there are 9 augmented amicable pairs with m<=10^6
%t A126161 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}]
%Y A126161 Cf. A007992, A015630.
%K A126161 hard,nonn
%O A126161 1,5
%A A126161 _Ant King_, Dec 20 2006