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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).

%I A354768 #21 Jan 04 2024 17:39:57
%S A354768 1,2,4,6,8,12,18,24,30,36,48,60,72,84,90,120,144,180,240,252,360,420,
%T A354768 480,504,540,720,840,900,1008,1080,1260,1440,1680,1800,2520,2640,2880,
%U A354768 3360,3780,3960,5040,5280,5400,5460,5544,6300,7560,7920,8400,10080,10920,12600,15120,15840,16380,18480
%N 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).
%C A354768 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
%D A354768 David desJardins, Posting to Math Fun Mailing List, Jun 21 2022.
%p A354768 N:= 10^6:
%p A354768 Q:= [seq(numtheory:-tau(k)/k, k=1..N)]:
%p A354768 V:= Vector(10^6):
%p A354768 r:= 2/10^3:
%p A354768 for n from 10^6 to 1 by -1 do
%p A354768 r:= max(Q[n],r);
%p A354768 V[n]:= r;
%p A354768 od:
%p A354768 select(i -> Q[i] >= V[i+1], [$1..10^6-1]); # _Robert Israel_, Jan 23 2023
%Y A354768 Cf. A000005, A066523, A354769, A368523.
%K A354768 nonn
%O A354768 1,2
%A A354768 _N. J. A. Sloane_, Jun 21 2022
%E A354768 More terms from _Robert Israel_, Jan 23 2023