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

4, 8, 16, 20, 28, 32, 40, 44, 48, 52, 56, 64, 68, 76, 80, 88, 92, 96, 100, 104, 112, 116, 124, 128, 136, 140, 148, 152, 160, 164, 172, 176, 184, 188, 192, 196, 200, 208, 212, 220, 224, 232, 236, 240

Offset: 1

Author

Gary Detlefs, Jan 28 2019

Keywords

• nonn

Comments

All terms are divisible by 4.

A092259 (numbers congruent to {4,8} (mod 12)) is a subset.

Sequence also includes all numbers of the form 48*k where k is congruent to {1,2} (mod 3) (A001651).

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,...}

From Robert Israel, Jan 29 2019: (Start)

Numbers k such that A007814(k)- 2*A007949(k) >= 2.

Sequence is closed under multiplication. (End)

The asymptotic density of this sequence is 2/11. - Amiram Eldar, Mar 25 2021

Examples

			tau(4*20) = 10, tau(3*20)=12. So 20 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001651, A007814, A007949, A092259.

Programs

Maple

with(numtheory): for n from 1 to 300 do if tau(4*n) < tau(3*n) then print(n) fi od

Mathematica

Select[Range[4, 240, 4], #1 < #2 & @@ DivisorSigma[0, # {4, 3}] &] (* Michael De Vlieger, Jan 29 2019 *)
Select[Range[240], IntegerExponent[#, 2] - 2 * IntegerExponent[#, 3] >= 2 &] (* Amiram Eldar, Mar 25 2021 *)