A354768 - OEIS

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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).

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..56.

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;