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A126161
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Number of augmented amicable pairs (m,n) with m<n and for which m<=10^k, k=1,2,3,...
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0
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0, 0, 0, 1, 4, 9, 36, 84, 188, 420, 930, 1931
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| J. M. Pedersen, Known amicable pairs.
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FORMULA
| An augmented amicable pair (m,n) is a pair of integers m, n with m<n and for which sigma(m)=sigma(n)=m+n-1
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EXAMPLE
| a(6)=9 because there are 9 augmented amicable pairs with m<=10^6
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MATHEMATICA
| s[n_]:=DivisorSigma[1, n]-n; AugmentedAmicableNumberQ[n_]:=If[s[s[n]+1]==n-1 && !DivisorSigma[1, n]==2n-1, True, False]; AugmentedAmicablePairList[ k_]:=(bnlist=Select[Range[k], AugmentedAmicableNumberQ[ # ]&]; newprlist= Table[Sort[{bnlist[[n]], s[bnlist[[n]]]+1}], {n, 1, Length[bnlist]}]; augamprlist=Union[newprlist, newprlist]); data=AugmentedAmicablePairList[10^7]; Table[Length[Select[data, First[ # ]<10^k &]], {k, 1, 7}]
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CROSSREFS
| Cf. A007992, A015630.
Sequence in context: A115700 A029806 A133125 * A179934 A018224 A149137
Adjacent sequences: A126158 A126159 A126160 * A126162 A126163 A126164
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KEYWORD
| hard,nonn
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AUTHOR
| Ant King (mathstutoring(AT)ntlworld.com), Dec 20 2006
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