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 A127663 Infinitary aspiring numbers. 2
 30, 42, 54, 66, 72, 78, 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, 516, 520, 532, 540, 542, 544, 550, 572, 576, 578, 586, 592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers whose infinitary aliquot sequences end in an infinitary perfect number, but are not infinitary perfect numbers themselves. LINKS Graeme L. Cohen, On an integer's infinitary divisors, Math. Comp., 54 (1990), 395-411. 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] EXAMPLE a(5)=72 because the fifth non-infinitary perfect number whose infinitary aliquot sequence ends in an infinitary perfect number is 72. MATHEMATICA 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[750], InfinitaryPerfectNumberQ[Last[iTrajectory[ # ]]] && !InfinitaryPerfectNumberQ[ # ]&] CROSSREFS Cf. A007357, A126168, A127661, A127662, A127664, A127665, A127666, A127667. Sequence in context: A103098 A110849 A074696 * A008885 A097036 A090790 Adjacent sequences:  A127660 A127661 A127662 * A127664 A127665 A127666 KEYWORD hard,nonn AUTHOR Ant King, Jan 26 2007 STATUS approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)