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Search: id:A127662
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| A127662 |
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Integers whose infinitary aliquot sequences end in an infinitary perfect number (A007357). |
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+0
5
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| 6, 30, 42, 54, 60, 66, 72, 78, 90, 100, 140, 148, 152, 192, 194, 196, 208, 220, 238, 244, 252, 268, 274, 292, 296, 298, 300, 336, 348, 350, 360, 364, 372, 374, 380, 382, 386, 400, 416, 420, 424, 476, 482, 492
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Cohen, Graeme L.; On an Integer's Infinitary Divisors, Mathematics of Computation, Vol. 54, No. 189. (Jan., 1990), pp. 395-411.
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LINKS
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Pedersen, Jan Munch, Tables of Aliquot Cycles.
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EXAMPLE
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a(5)=60 because the fifth number whose infinitary aliquot sequence ends in an infinitary perfect number is 60.
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MATHEMATICA
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ExponentList[n_Integer, factors_List]:={#, IntegerExponent[n, # ]}&/@factors; InfinitaryDivisors[1]:={1}; InfinitaryDivisors[n_Integer?Positive]:=Module[ { factors=First/@FactorInteger[n], d=Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f, g}, BitOr[f, g]==g][ #, Last[ # ]]]&/@ Transpose[Last/@ExponentList[ #, factors]&/@d]], _?(And@@#&), {1}]] ]] ] Null; properinfinitarydivisorsum[k_]:=Plus@@InfinitaryDivisors[k]-k; g[n_] := If[n > 0, properinfinitarydivisorsum[n], 0]; iTrajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]; InfinitaryPerfectNumberQ[0]=False; InfinitaryPerfectNumberQ[k_Integer] :=If[properinfinitarydivisorsum[k]==k, True, False]; Select[Range[500], InfinitaryPerfectNumberQ[Last[iTrajectory[ # ]]] &]
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CROSSREFS
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Cf. A007357, A126168, A127661, A127663, A127664, A127665, A127666, A127667.
Adjacent sequences: A127659 A127660 A127661 this_sequence A127663 A127664 A127665
Sequence in context: A002445 A027762 A130512 this_sequence A003062 A101937 A101939
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KEYWORD
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hard,nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Jan 26 2007
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