A066642 a(n) = floor(n^(n/2)).

1, 1, 2, 5, 16, 55, 216, 907, 4096, 19683, 100000, 534145, 2985984, 17403307, 105413504, 661735513, 4294967296, 28761784747, 198359290368, 1406563064942, 10240000000000, 76436817165460, 584318301411328, 4569515072723572, 36520347436056576, 298023223876953125

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..702 (terms n=1..150 from Harry J. Smith)

Example

a(5) = 55 as {5^(1/2)}^5 = 55.9016994374947424102293417182819...

Maple

a:= n-> floor(n^(n/2)):
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 08 2025

Mathematica

Table[ Floor[Sqrt[n]^n], {n, 1, 25} ]

Prog

(PARI) a(n) = sqrtint(n^n); \\ Michel Marcus, Nov 01 2022
(Magma) [Floor(n^(n/2)): n in [1..25]]; // G. C. Greubel, Dec 30 2017
(Python)
from math import isqrt
def A066642(n): return isqrt(n**n) # Chai Wah Wu, Jun 08 2025

Crossrefs

Cf. A092503, A147771, A190343.

Bisection gives A062971 (even part).

Sequence in context: A149972 A026106 A308027 * A333233 A019988 A137732

Adjacent sequences: A066639 A066640 A066641 * A066643 A066644 A066645

Keyword

easy,nonn

Author

Amarnath Murthy, Dec 29 2001

Extensions

More terms from Robert G. Wilson v, Jan 03 2002

a(0)=1 prepended by Alois P. Heinz, Jun 08 2025

Status

approved