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<n.

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

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..13.

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.

Example

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

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}]

Crossrefs

Cf. A003502, A003503, A005276.

Sequence in context: A230314 A220263 A033492 * A118962 A096033 A073413

Adjacent sequences: A126157 A126158 A126159 * A126161 A126162 A126163

Keyword

nonn,hard,more

Author

Ant King, Dec 19 2006

Extensions

a(13) from Giovanni Resta, Jul 24 2019

Status

approved