A002821 -id:A002821 - cp's OEIS frontend

A000093 a(n) = floor(n^(3/2)).

0, 1, 2, 5, 8, 11, 14, 18, 22, 27, 31, 36, 41, 46, 52, 58, 64, 70, 76, 82, 89, 96, 103, 110, 117, 125, 132, 140, 148, 156, 164, 172, 181, 189, 198, 207, 216, 225, 234, 243, 252, 262, 272, 281, 291, 301, 311, 322, 332, 343, 353, 364, 374, 385, 396, 407, 419, 430

Offset: 0

N. J. A. Sloane

B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Christian G. Bower, Table of n, a(n) for n=0..500
B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216. [Annotated scanned copy]

Integer part of square root of n^k: A000196 (k=1), this sequence (k=3), A155013 (k=5), A155014 (k=7), A155015 (k=11), A155016 (k=13), A155018 (k=15), A155019 (k=17).
Cf. A002821.
Cf. A185549.

a000093 = a000196 . a000578  -- Reinhard Zumkeller, Jul 11 2014

Digits := 100: A000093 := n->floor(evalf(n^(3/2)));

Mathematica
```
Table[ Floor[ Sqrt[n^3]], {n, 0, 60}]
```
PARI
```
a(n)=if(n<0,0,sqrtint(n^3))
```

from math import isqrt
def A000093(n): return isqrt(n**3) # Chai Wah Wu, Sep 08 2024

a(n) = A077121(n) - 1. [Reinhard Zumkeller, Oct 31 2009]
a(n) = floor(n*sqrt(n)). [Arkadiusz Wesolowski, Jun 01 2011]
a(n) = A000196(A000578(n)) = A074704(n)+n*A000196(n). [Reinhard Zumkeller, Jun 27 2011]

More terms from James Sellers, May 04 2000

A077118 Nearest integer square to n^3.

Original entry on oeis.org

0, 1, 9, 25, 64, 121, 225, 361, 529, 729, 1024, 1296, 1764, 2209, 2704, 3364, 4096, 4900, 5776, 6889, 7921, 9216, 10609, 12100, 13924, 15625, 17689, 19600, 21904, 24336, 26896, 29929, 32761, 36100, 39204, 42849, 46656, 50625, 54756, 59536

Offset: 0

Reinhard Zumkeller, Oct 29 2002

nonn

			a(5)=121, as 121=11^2 is the nearest square to 125=5^3.

Cf. A000290, A000578, A002821, A077119, A077110.

Table[Round[Sqrt[n^3]]^2, {n, 0, 39}] (* Alonso del Arte, Dec 07 2011, based on Artur Jasinski's program for A077119 *)

from math import isqrt
def A077118(n): return ((m:=isqrt(k:=n**3))+int((k-m*(m+1)<<2)>=1))**2 # Chai Wah Wu, Jul 29 2022

a(n) = if A077116(n) < A070929(n) then A065733(n) else A077115(n).

a(n) = A002821(n)^2. - Chai Wah Wu, Jul 30 2022

A054846 Nearest integer to n^(2/3).

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18

Offset: 0

Henry Bottomley, Apr 14 2000

Cf. A002821, A054847, A054848.

Digits := 100; [ seq(round(eval(n^(2/3))), n=0..100) ];

A054847 Nearest integer to (nearest integer to n^(2/3))^(3/2).

Original entry on oeis.org

0, 1, 3, 3, 5, 5, 5, 8, 8, 8, 11, 11, 11, 15, 15, 15, 15, 19, 19, 19, 19, 23, 23, 23, 23, 27, 27, 27, 27, 27, 32, 32, 32, 32, 32, 36, 36, 36, 36, 42, 42, 42, 42, 42, 42, 47, 47, 47, 47, 47, 52, 52, 52, 52, 52, 52, 58, 58, 58, 58, 58, 58, 64, 64, 64, 64, 64, 64, 70, 70, 70, 70

Offset: 0

Henry Bottomley, Apr 14 2000

Cf. A002821, A054846, A054848.

a(n)=A002821(A054846(n))

A054848 n - nearest integer to (nearest integer to n^(2/3))^(3/2).

Original entry on oeis.org

0, 0, -1, 0, -1, 0, 1, -1, 0, 1, -1, 0, 1, -2, -1, 0, 1, -2, -1, 0, 1, -2, -1, 0, 1, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -1, 0, 1, 2, -3, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, 3, -2, -1, 0, 1, 2, 3, -2, -1, 0, 1, 2, 3, -2, -1, 0, 1, 2, 3, -2, -1, 0, 1, 2, 3, -3, -2, -1, 0, 1, 2, 3, -2

Offset: 0

Henry Bottomley, Apr 14 2000

Cf. A002821, A054846, A054847.

a(n) = n-A002821(A054846(n)) = n-A054847(n)

cp's OEIS Frontend

A000093 a(n) = floor(n^(3/2)).

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A077118 Nearest integer square to n^3.

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Programs

Mathematica

Python

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A054846 Nearest integer to n^(2/3).

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Author

Keywords

Crossrefs

Programs

Maple

A054847 Nearest integer to (nearest integer to n^(2/3))^(3/2).

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Author

Keywords

Crossrefs

Formula

A054848 n - nearest integer to (nearest integer to n^(2/3))^(3/2).

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