A122221 Largest number k such that k! < (n!)^n.

2, 5, 8, 13, 19, 25, 32, 41, 50, 60, 72, 84, 97, 111, 126, 142, 159, 177, 196, 216, 237, 259, 282, 306, 330, 356, 383, 410, 439, 469, 499, 531, 563, 597, 631, 667, 703, 740, 779, 818, 858, 899, 942, 985, 1029, 1074, 1120, 1167, 1215, 1264, 1314, 1365, 1417

Offset

2,1

Links

Chai Wah Wu, Table of n, a(n) for n = 2..10000

Example

a(3)=5 because 5! = 120 is less than (3!)^3 = 216 whereas 6! = 720 > 216.

Maple

a:=proc(n) local b: b:=proc(k) if k!<(n!)^n then k else fi end: max(seq(b(k), k=1..2200)) end: seq(a(n), n=2..67); # Emeric Deutsch, Oct 07 2006

Mathematica

s={}; Do[k=1; Until[k!>=(n!)^n, k++]; AppendTo[s, k-1], {n, 2, 54}]; s (* James C. McMahon, Oct 26 2024 *)

Crossrefs

Cf. A036740, A121347, A122222.

Sequence in context: A000982 A289751 A200274 * A083704 A111097 A027916

Adjacent sequences: A122218 A122219 A122220 * A122222 A122223 A122224

Keyword

nonn

Author

Hugo Pfoertner, Sep 25 2006

Extensions

More terms from Emeric Deutsch, Oct 07 2006

Status

approved