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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 8 14:30 EST 2023. Contains 367679 sequences. (Running on oeis4.)