A185549 -id:A185549 - cp's OEIS frontend

A185550 Numbers not of the form ceiling(n^(3/2)); complement of A185549.

2, 4, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 147, 148, 150

Offset: 1

Clark Kimberling, Jan 30 2011

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A185549, A185543.

import Data.List.Ordered (minus)
a185550 n = a185550_list !! (n-1)
a185550_list = [0..] `minus` a185549_list
-- Reinhard Zumkeller, Jul 24 2015

f[n_]=Ceiling[n^(3/2)];
t1=Table[f[n],{n,1,90}];t1  (* A185549 *)
t2=Complement[Range[150], Table[f[n],{n,1,80}]];t2  (* A185550 *)

from sympy import integer_nthroot
def A185550(n):
    def f(x): return n+integer_nthroot(x**2,3)[0]
    def iterfun(f,n=0):
        m, k = n, f(n)
        while m != k: m, k = k, f(k)
        return m
    return iterfun(f,n) # Chai Wah Wu, Sep 09 2024

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

Original entry on oeis.org

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

A077115 Least integer square >= n^3.

Original entry on oeis.org

0, 1, 9, 36, 64, 144, 225, 361, 529, 729, 1024, 1369, 1764, 2209, 2809, 3481, 4096, 5041, 5929, 6889, 8100, 9409, 10816, 12321, 13924, 15625, 17689, 19881, 22201, 24649, 27225, 29929, 33124, 36100, 39601, 43264, 46656, 51076, 55225, 59536

Offset: 0

Reinhard Zumkeller, Oct 29 2002

			a(10) = 1024, as 1024 = 32^2 is the least square >= 1000 = 10^3.

Cf. A000290, A000578, A048761, A065733, A077107, A077118, A185549.

[Ceiling(n^(3/2))^2: n in [0..50]]; // Vincenzo Librandi, Feb 17 2015

lis[n_]:=Module[{c=Sqrt[n^3]},If[IntegerQ[c],c^2,(Floor[c]+1)^2]]; Array[lis,40,0] (* Harvey P. Dale, Jan 22 2013 *)

a(n) - A070929(n) = n^3.
a(n) = ceiling(n^(3/2))^2. - Benoit Cloitre, Nov 01 2002
a(n) = A185549(n)^2. - Amiram Eldar, May 17 2025
a(n) = A048761(n^3). - Michel Marcus, May 17 2025

A144968 Number of squares between consecutive cubes.

Original entry on oeis.org

1, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 5, 7, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 9, 9, 8, 10, 9, 9, 9, 10, 10, 9, 10, 10, 10, 11, 10, 10, 11, 11, 10, 11, 11, 11, 12, 11, 11, 12, 11, 12, 12, 12, 11, 13, 12, 12, 12, 13, 12, 13, 12, 13, 13, 13, 13, 13, 13, 14, 13, 13, 14, 14

Offset: 0

Reinhard Zumkeller, Sep 27 2008, Sep 29 2008

nonn

a(n) = sum {A010052(k): n^3 <= k < (n+1)^3}. - Reinhard Zumkeller, Jul 24 2015, corrected.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A000290, A000578, A077115.

Cf. A010052, A185549.

a144968 n = a144968_list !! n
a144968_list = zipWith (-) (tail a185549_list) a185549_list
-- Reinhard Zumkeller, Jul 24 2015

Last[#]-First[#]&/@Partition[Table[Ceiling[n^(3/2)],{n,0,90}],2,1] (* Harvey P. Dale, Jul 10 2013 *)

for(n=0,50, print1(ceil((n+1)^(3/2)) - ceil(n^(3/2)), ", ")) \\ G. C. Greubel, Jul 08 2017

a(n) = ceiling((n+1)^(3/2)) - ceiling(n^(3/2)).

cp's OEIS Frontend

A185550 Numbers not of the form ceiling(n^(3/2)); complement of A185549.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Python

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

Views

Author

Keywords

References

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Formula

Extensions

A077115 Least integer square >= n^3.

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Mathematica

Formula

A144968 Number of squares between consecutive cubes.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula