A066642
a(n) = floor(n^(n/2)).
Original entry on oeis.org
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
a(5) = 55 as {5^(1/2)}^5 = 55.9016994374947424102293417182819...
Bisection gives
A062971 (even part).
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[Floor(n^(n/2)): n in [1..25]]; // G. C. Greubel, Dec 30 2017
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a:= n-> floor(n^(n/2)):
seq(a(n), n=0..25); # Alois P. Heinz, Jun 08 2025
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Table[ Floor[Sqrt[n]^n], {n, 1, 25} ]
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a(n) = sqrtint(n^n); \\ Michel Marcus, Nov 01 2022
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from math import isqrt
def A066642(n): return isqrt(n**n) # Chai Wah Wu, Jun 08 2025
A271390
a(n) = (2*n + 1)^(2*floor((n-1)/2) + 1).
Original entry on oeis.org
1, 3, 5, 343, 729, 161051, 371293, 170859375, 410338673, 322687697779, 794280046581, 952809757913927, 2384185791015625, 4052555153018976267, 10260628712958602189, 23465261991844685929951, 59938945498865420543457, 177482997121587371826171875, 456487940826035155404146917
Offset: 0
a(0) = 1;
a(1) = 3^1 = 3;
a(2) = 5^1 = 5;
a(3) = 7^3 = 343;
a(4) = 9^3 = 729;
a(5) = 11^5 = 161051;
a(6) = 13^5 = 371293;
a(7) = 15^7 = 170859375;
a(8) = 17^7 = 410338673;
...
a(10000) = 1.644...*10^43006;
...
a(100000) = 8.235...*10^530097, etc.
This sequence can be represented as a binary tree:
1
................../ \..................
3^1 5^1
7^3......../ \......9^3 11^5....../ \.......13^5
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
15^7 17^7 19^9 21^9 23^11 25^11 27^13 29^13
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A271390:=n->(2*n + 1)^(n - 1/2 - (-1)^n/2): seq(A271390(n), n=0..30); # Wesley Ivan Hurt, Apr 10 2016
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Table[(2 n + 1)^(2 Floor[(n - 1)/2] + 1), {n, 0, 18}]
Table[(2 n + 1)^(n - 1 + (1 + (-1)^(n - 1))/2), {n, 0, 18}]
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a(n) = (2*n + 1)^(2*((n-1)\2) + 1); \\ Altug Alkan, Apr 06 2016
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for n in range(0,10**3):print((int)((2*n+1)**(2*floor((n-1)/2)+1)))
# Soumil Mandal, Apr 10 2016
Showing 1-2 of 2 results.
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