login
A347064
Smallest number with at least 2^n divisors.
2
1, 2, 6, 24, 120, 840, 7560, 83160, 1081080, 17297280, 294053760, 5587021440, 128501493120, 3212537328000, 93163582512000, 2888071057872000, 106858629141264000, 4381203794791824000, 184010559381256608000, 7912454053394034144000, 371885340509519604768000
OFFSET
0,2
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.
LINKS
FORMULA
a(n) = A061799(2^n). - Michel Marcus, Aug 16 2021
EXAMPLE
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Aug 15 2021
STATUS
approved