A155013 Integer part of square root of n^5 = A000584(n).

1, 5, 15, 32, 55, 88, 129, 181, 243, 316, 401, 498, 609, 733, 871, 1024, 1191, 1374, 1573, 1788, 2020, 2270, 2536, 2821, 3125, 3446, 3787, 4148, 4528, 4929, 5350, 5792, 6255, 6740, 7247, 7776, 8327, 8901, 9498, 10119, 10763, 11432, 12124, 12841, 13584, 14351

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 19 2009

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000093.

Integer part of square root of n^k: A000196 (k=1), A000093 (k=3), this sequence (k=5), A155014 (k=7), A155015 (k=11), A155016 (k=13), A155018 (k=15), A155019 (k=17),

Programs

Magma

[Floor(Sqrt(n^5)): n in [1..30]]; // G. C. Greubel, Dec 30 2017

Mathematica

a={};Do[AppendTo[a,IntegerPart[(n^5)^(1/2)]],{n,5!}];a
IntegerPart[Sqrt[Range[50]^5]] (* Harvey P. Dale, May 14 2012 *)
Table[Floor[Sqrt[n^5]], {n,1,30}] (* G. C. Greubel, Dec 30 2017 *)

PARI

for(n=1,30, print1(sqrtint(n^5), ", ")) \\ G. C. Greubel, Dec 30 2017

Python

from math import isqrt
def A155013(n): return isqrt(n**5) # Chai Wah Wu, Aug 08 2025

Formula

a(n) = floor(n^2 * sqrt(n)). - Davide Rotondo, Dec 01 2024