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Cf. A002182, A000005, A004394, A354768.

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Crowded numbers: for any nk in the sequence, d(nk)/nk is larger than d(m)/m for all m > nk.

Since d(m) < 2*sqrt(m), we need only test values of m < (2n2k/d(nk))^2.

Additional comments from Roy Maulbogat, Jan 22 2008: (Start)

Additional comments from Roy Maulbogat, Jan 22 2008: (Start) It can easily be shown that all crowded numbers are even and that there is always a crowded number between N and 2N. This allows us to improve the algorithm as followfollows:

crowded[nk_] := Module[{},

* If[OddQ[nk], Return [False]];*

div = DivisorSigma[0,nk]/nk;

For [ *m=nk+2, m<=2n2k, m+=2*, If[

On second thought, it might be wise to use Min[2n2k, stop] as the stopping condition of the loop ("stop" being the variable defined in the original algorithm). (End)

Roy Maulbogat and Donovan Johnson, <a href="/A066523/b066523.txt">Table of n, a(n) for n = 1..300</a> (first 129 terms from Roy Maulbogat)

Edited by Dean Hickerson, Jan 07, 2002.

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On second thought, it might be wise to use Min[2n, stop] as the stoopingstopping condition of the loop ("stop" being the variable defined in the original algorithm). (End)

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Edited by _Dean Hickerson (dean.hickerson(AT)yahoo.com), _, Jan 07, 2002.

OEIS Server: https://oeis.org/edit/global/2238

Roy Maulbogat and Donovan Johnson, <a href="/A066523/b066523_1.txt">Table of n, a(n) for n = 1..300</a> (first 129 terms from Roy Maulbogat)

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OEIS Server: Installed new b-file as b066523.txt.  Old b-file is now b066523_1.txt.