A347064 Smallest number with at least 2^n divisors.

1, 2, 6, 24, 120, 840, 7560, 83160, 1081080, 17297280, 294053760, 5587021440, 128501493120, 3212537328000, 93163582512000, 2888071057872000, 106858629141264000, 4381203794791824000, 184010559381256608000, 7912454053394034144000, 371885340509519604768000

Offset: 0

Author

Jon E. Schoenfield, Aug 15 2021

Keywords

• nonn

Comments

Begins to differ from A037992 at n=18; a(18) < A037992(18), but the number of divisors d(a(18)) = 276480 > 262144 = 2^18.

Examples

			   n                A037992(n)                      a(n)  d(a(n))      2^n
  --  ------------------------  ------------------------  -------  -------
  18     188391763176048432000     184010559381256608000   276480   262144
  19    8854412869274276304000    7912454053394034144000   552960   524288
  20  433866230594439538896000  371885340509519604768000  1105920  1048576
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..356

Crossrefs

Cf. A000005, A000079, A037992, A061799.

Programs

Mathematica

Table[SelectFirst[Table[{n,DivisorSigma[0,n]},{n,0,11*10^5}],#[[2]]==2^k&],{k,0,8}][[;;,1]] (* The program generates the first nine terms of the sequence. *)  (* Harvey P. Dale, Feb 04 2024 *)

Formula

a(n) = A061799(2^n). - Michel Marcus, Aug 16 2021