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
Offset: 1
Keywords
References
- David desJardins, Posting to Math Fun Mailing List, Jun 21 2022.
Programs
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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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