A214449 Least m>0 such that n! <= m^m.

1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 51, 52

Offset: 1

Author

Clark Kimberling, Jul 18 2012

Keywords

• nonn
• easy

Comments

Conjecture: this sequence results from A118168 by deleting the first two 1s.

Examples

			a(4) = 3 because 2^2 < 4! < 3^3.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A214046.

Programs

Mathematica

Table[m = 1; While[n! > m^m, m++]; m, {n, 1, 100}]