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
Examples
a(5) = 55 as {5^(1/2)}^5 = 55.9016994374947424102293417182819...
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..702 (terms n=1..150 from Harry J. Smith)
Programs
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Magma
[Floor(n^(n/2)): n in [1..25]]; // G. C. Greubel, Dec 30 2017
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Maple
a:= n-> floor(n^(n/2)): seq(a(n), n=0..25); # Alois P. Heinz, Jun 08 2025
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Mathematica
Table[ Floor[Sqrt[n]^n], {n, 1, 25} ] -
PARI
a(n) = sqrtint(n^n); \\ Michel Marcus, Nov 01 2022
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Python
from math import isqrt def A066642(n): return isqrt(n**n) # Chai Wah Wu, Jun 08 2025
Extensions
More terms from Robert G. Wilson v, Jan 03 2002
a(0)=1 prepended by Alois P. Heinz, Jun 08 2025