A036493 Largest number having binary order n (A029837) and of which the number of divisors is maximal in that range of g(k) = n.

1, 2, 4, 8, 12, 30, 60, 120, 240, 504, 840, 1680, 3960, 7560, 15120, 32760, 65520, 131040, 262080, 498960, 997920, 1965600, 3603600, 7207200, 14414400, 32432400, 64864800, 122522400, 245044800, 514594080, 1029188160, 2095133040, 4227022800, 8454045600

Offset: 0

Author

Labos Elemer

Keywords

• nonn

Comments

This sequence differs from A036451 only at n = 3, 5, 9, 12, and 15, which are the values of n for which there exists more than one k such that g(k) = n and d(k) has the maximum possible value.

a(n) is the largest term k in A067128 such that log_2(k) <= n. - Jon E. Schoenfield, May 13 2018

Examples

			For n = 9, k is in {257, 512}, max(d(k)) = 24 (see A036451); this holds for four different numbers (360, 420, 480, and 504); a(9) = 504 since it is the largest.
		

Crossrefs

Cf. A000005, A029837, A005179, A007416, A036451, A036470, A036484.

Programs

Mathematica

{1}~Join~Table[Max@ MaximalBy[Range[2^(n - 1) + 1, 2^n], DivisorSigma[0, #] &], {n, 24}] (* Michael De Vlieger, Aug 01 2017 *)

Extensions

a(22)-a(24) from Michael De Vlieger, Aug 01 2017

a(25)-a(33) from Jon E. Schoenfield, May 12 2018