%I #15 Nov 18 2019 14:59:48

%S 0,1,2,8,9,17,46,79,180,404,882,1946,4122

%N Number of betrothed pairs (m,n) with m <=10^k (and k=1,2,3,...), where a betrothed pair satisfies sigma(m)=sigma(n)=m+n+1 and m<n.

%C Also called quasi-amicable pairs, or reduced amicable pairs.

%H J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]

%H J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Via Internet Archive Wayback-Machine]

%H J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]

%H P. Pollack, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Pollack/pollack3.html">Quasi-Amicable Numbers are Rare</a>, J. Int. Seq. 14 (2011) # 11.5.2.

%e a(7)=46 because there are 46 betrothed pairs (m,n) with m<=10^7

%t s[n_]:=DivisorSigma[1,n]-n;BetrothedNumberQ[n_]:=If[s[s[n]-1]==n+1 && n>1,True,False];BetrothedPairList[k_]:=(anlist=Select[Range[k],BetrothedNumberQ[ # ] &]; prlist=Table[Sort[{anlist[[n]],s[anlist[[n]]]-1}],{n,1,Length[anlist]}]; Union[prlist,prlist]);data=BetrothedPairList[10^6];Table[Length[Select[data,First[ # ]<10^k &]],{k,1,6}]

%Y Cf. A003502, A003503, A005276.

%K nonn,hard,more

%O 1,3

%A _Ant King_, Dec 19 2006

%E a(13) from _Giovanni Resta_, Jul 24 2019