A190343 -id:A190343 - cp's OEIS frontend

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

Amarnath Murthy, Dec 29 2001

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

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

Cf. A092503, A147771, A190343.

Bisection gives A062971 (even part).

[Floor(n^(n/2)): n in [1..25]]; // G. C. Greubel, Dec 30 2017

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} ]
```

a(n) = sqrtint(n^n); \\ Michel Marcus, Nov 01 2022

from math import isqrt
def A066642(n): return isqrt(n**n) # Chai Wah Wu, Jun 08 2025

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

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

A075364 a(n) = floor( geometric mean of n-th row of A075363).

Original entry on oeis.org

1, 2, 9, 32, 125, 529, 2401, 11585, 59049, 316227, 1771561, 10343751, 62748517, 394421215, 2562890625, 17179869184, 118587876497, 841567195983, 6131066257801, 45794672179195, 350277500542221, 2740695769692949

Offset: 1

Amarnath Murthy, Sep 20 2002

nonn

G. C. Greubel, Table of n, a(n) for n = 1..500 (terms 1..100 from Vincenzo Librandi)

Cf. A075363, A147771, A190343.

[Floor(n^((n+1)/2)): n in [1..30]]; // Vincenzo Librandi, May 07 2011

Table[Floor[n^((n + 1)/2)], {n,1,50}] (* G. C. Greubel, Dec 30 2017 *)

for(n=1, 30, print1(floor(n^((n+1)/2)), ", ")) \\ G. C. Greubel, Dec 30 2017

from math import isqrt
def A075364(n): return isqrt(n**(n+1)) # Chai Wah Wu, Jun 08 2025

a(n) = floor(n^((n+1)/2)).

More terms from Sascha Kurz, Jan 12 2003

A255616 Table read by antidiagonals, T(n,k) = floor(sqrt(k^n)), n >= 0, k >=1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 4, 5, 4, 1, 1, 2, 5, 8, 9, 5, 1, 1, 2, 6, 11, 16, 15, 8, 1, 1, 2, 7, 14, 25, 32, 27, 11, 1, 1, 3, 8, 18, 36, 55, 64, 46, 16, 1, 1, 3, 9, 22, 49, 88, 125, 128, 81, 22, 1, 1, 3, 10, 27, 64, 129, 216, 279, 256, 140, 32, 1, 1, 3, 11, 31, 81, 181, 343, 529, 625, 512, 243, 45, 1

Offset: 0

Kival Ngaokrajang, Feb 28 2015

			See table in the links.

G. C. Greubel, Table of n, a(n) for the first 100 antidaigonals, flattened
Kival Ngaokrajang, Example of table T(n,k), n = 0..12, k = 1..10

Rows(1..10): A000012, A000196, A000027, A000093, A000290, A155013, A000578, A155014, A000583, A238170.
Columns(1..10): A000012, A017910, A017913, A000079, A017919, A017922, A017925, A017928, A000244, A017934.
Diagonals: A190343, A066642, A075264.

T[n_, k_] := Floor[Sqrt[k^n]]; Table[T[k, n + 1 - k], {n, 0, 15}, {k, 0, n}] (* G. C. Greubel, Dec 30 2017 *)

{for(i=1,20,for(n=0,i-1,a=floor(sqrt((i-n)^n));print1(a,", ")))}

T(n,k) = floor(sqrt(k^n)), n >= 0, k >=1.

Terms a(81) onward added by G. C. Greubel, Dec 30 2017

cp's OEIS Frontend

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

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A075364 a(n) = floor( geometric mean of n-th row of A075363).

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A255616 Table read by antidiagonals, T(n,k) = floor(sqrt(k^n)), n >= 0, k >=1.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions