cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A354768 Numbers k such that d(k)/k >= d(m)/m for all m > k, where d(k) is the number-of-divisors function A000005(k).

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 18, 24, 30, 36, 48, 60, 72, 84, 90, 120, 144, 180, 240, 252, 360, 420, 480, 504, 540, 720, 840, 900, 1008, 1080, 1260, 1440, 1680, 1800, 2520, 2640, 2880, 3360, 3780, 3960, 5040, 5280, 5400, 5460, 5544, 6300, 7560, 7920, 8400, 10080, 10920, 12600, 15120, 15840, 16380, 18480
Offset: 1

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Author

N. J. A. Sloane, Jun 21 2022

Keywords

Comments

Because of the bound d(m) <= 2*sqrt(m), in order for k to be in the sequence it suffices that d(k)/k >= d(m)/m for k < m < (2*k/d(k))^2. - Robert Israel, Jan 23 2023

References

  • David desJardins, Posting to Math Fun Mailing List, Jun 21 2022.

Crossrefs

Programs

  • Maple
    N:= 10^6:
    Q:= [seq(numtheory:-tau(k)/k, k=1..N)]:
    V:= Vector(10^6):
    r:= 2/10^3:
    for n from 10^6 to 1 by -1 do
    r:= max(Q[n],r);
    V[n]:= r;
    od:
    select(i -> Q[i] >= V[i+1], [$1..10^6-1]); # Robert Israel, Jan 23 2023

Extensions

More terms from Robert Israel, Jan 23 2023
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