cp's OEIS Frontend

A306199 Numbers k having the property that tau(4*k) < tau(3*k) where tau = A000005.

%I A306199 #29 Mar 25 2021 04:56:40
%S A306199 4,8,16,20,28,32,40,44,48,52,56,64,68,76,80,88,92,96,100,104,112,116,
%T A306199 124,128,136,140,148,152,160,164,172,176,184,188,192,196,200,208,212,
%U A306199 220,224,232,236,240
%N A306199 Numbers k having the property that tau(4*k) < tau(3*k) where tau = A000005.
%C A306199 All terms are divisible by 4.
%C A306199 A092259 (numbers congruent to {4,8} (mod 12)) is a subset.
%C A306199 Sequence also includes all numbers of the form 48*k where k is congruent to {1,2} (mod 3) (A001651).
%C A306199 Additional entries of the form 48k, where k is divisible by three have k values of 12*{1,2,4,5,7,8,10,11,12,13,14,16,17,19,20,22,23,24,...}
%C A306199 From _Robert Israel_, Jan 29 2019: (Start)
%C A306199 Numbers k such that A007814(k)- 2*A007949(k) >= 2.
%C A306199 Sequence is closed under multiplication. (End)
%C A306199 The asymptotic density of this sequence is 2/11. - _Amiram Eldar_, Mar 25 2021
%H A306199 Robert Israel, <a href="/A306199/b306199.txt">Table of n, a(n) for n = 1..10000</a>
%e A306199 tau(4*20) = 10, tau(3*20)=12. So 20 is in the sequence.
%p A306199 with(numtheory): for n from 1 to 300 do if tau(4*n) < tau(3*n) then print(n) fi od
%t A306199 Select[Range[4, 240, 4], #1 < #2 & @@ DivisorSigma[0, # {4, 3}] &] (* _Michael De Vlieger_, Jan 29 2019 *)
%t A306199 Select[Range[240], IntegerExponent[#, 2] - 2 * IntegerExponent[#, 3] >= 2 &] (* _Amiram Eldar_, Mar 25 2021 *)
%Y A306199 Cf. A000005, A001651, A007814, A007949, A092259.
%K A306199 nonn
%O A306199 1,1
%A A306199 _Gary Detlefs_, Jan 28 2019