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A126160
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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.
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0
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0, 1, 2, 8, 9, 17, 46, 79, 180, 404, 882, 1946
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| J. O. M. Pedersen, Tables of aliquot cycles.
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EXAMPLE
| a(7)=46 because there are 46 betrothed pairs (m,n) with m<=10^7
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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}]
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CROSSREFS
| Cf. A003502, A003503, A005276.
Sequence in context: A004999 A105125 A033492 * A118962 A096033 A073413
Adjacent sequences: A126157 A126158 A126159 * A126161 A126162 A126163
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KEYWORD
| hard,nonn
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AUTHOR
| Ant King (mathstutoring(AT)ntlworld.com), Dec 19 2006
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