A126160 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

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

Offset: 1

Author

Ant King, Dec 19 2006

Keywords

• nonn
• hard
• more

Comments

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

Examples

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

Links

• J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]
• J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]
• J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]
• P. Pollack, Quasi-Amicable Numbers are Rare, J. Int. Seq. 14 (2011) # 11.5.2.

Crossrefs

Cf. A003502, A003503, A005276.

Programs

Mathematica

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}]

Extensions

a(13) from Giovanni Resta, Jul 24 2019