A100196 -id:A100196 - cp's OEIS frontend

A077106 Largest integer cube <= n^2.

0, 1, 1, 8, 8, 8, 27, 27, 64, 64, 64, 64, 125, 125, 125, 216, 216, 216, 216, 343, 343, 343, 343, 512, 512, 512, 512, 729, 729, 729, 729, 729, 1000, 1000, 1000, 1000, 1000, 1331, 1331, 1331, 1331, 1331, 1728, 1728, 1728, 1728, 1728, 2197, 2197

Offset: 0

Reinhard Zumkeller, Oct 29 2002

			a(20) = 343, as 343 = 7^3 is the largest cube <= 400 = 20^2.

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A000578, A000290, A065733, A075847, A077107, A077110, A077113.

a[n_] := Floor[Surd[n^2, 3]]^3; Array[a, 100, 0] (* Amiram Eldar, Apr 05 2025 *)

a(n) + A075847(n) = n^2.

a(n) = A100196(n)^3. - Amiram Eldar, Apr 06 2025

A032514 Sum of the integer part of 3/2-th roots of integers less than n.

Original entry on oeis.org

0, 1, 2, 4, 6, 8, 11, 14, 18, 22, 26, 30, 35, 40, 45, 51, 57, 63, 69, 76, 83, 90, 97, 105, 113, 121, 129, 138, 147, 156, 165, 174, 184, 194, 204, 214, 224, 235, 246, 257, 268, 279, 291, 303, 315, 327, 339, 352, 365, 378, 391, 404, 417, 431, 445, 459, 473, 487

Offset: 0

Michel Tixier (tixier(AT)dyadel.net)

nonn

Robert Israel, Table of n, a(n) for n = 0..10000

Partial sums of A100196.

ListTools:-PartialSums([seq(floor(n^(2/3)),n=0..100)]); # Robert Israel, Nov 11 2019

A077113 Number of nonnegative integer cubes <= n^2.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 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, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19

Offset: 0

Reinhard Zumkeller, Oct 29 2002

a(n) is the least number m such that m^3 > n^2. - Zak Seidov, May 03 2005

			Cubes <= 10^2: 0, 1, 8, 27 and 64, hence a(10) = 5.

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A026409, A026414, A054071, A077106, A077121, A100196.

Table[Floor[n^(2/3) + 1], {n, 0, 100}] (* Zak Seidov, May 03 2005 *)

from sympy import integer_nthroot
def A077113(n): return integer_nthroot(n**2,3)[0]+1 # Chai Wah Wu, Aug 15 2025

a(n) = floor(n^(2/3))+1.
a(n) = [x^(n^2)] (1/(1 - x))*Sum_{k>=0} x^(k^3). - Ilya Gutkovskiy, Apr 20 2018
a(n) = A100196(n) + 1. - Amiram Eldar, Apr 05 2025

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

A121536 Smallest m such that m^3 >= n^2.

Original entry on oeis.org

0, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 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, 18, 19, 19

Offset: 1

Zak Seidov, Aug 05 2006

Cf. A070923, A077107, A100196.

Mathematica
```
Table[Ceiling[n^(2/3)],{n,1,100}]
```

a(n) = ceiling(n^(2/3)).
a(n) = (A070923(n)+n^2)^(1/3).
If n is a cube a(n) = A100196(n), otherwise a(n) = A100196(n)+1.
a(n) = A077107(n)^(1/3). - Amiram Eldar, May 17 2025

Offset changed to 0 and a(0) prepended by Amiram Eldar, May 17 2025

A062108 a(n) = floor(n^(3/4)).

Original entry on oeis.org

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25

Offset: 0

Henry Bottomley, May 30 2001

			a(100) = floor(100^(3/4)) = floor(1000000^(1/4)) = floor(31.62...) = 31.

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A000196, A061054, A100196.

seq(floor(n^(3/4)),n=0..90); # Muniru A Asiru, Jul 01 2018

Floor[Range[0,80]^(3/4)] (* Harvey P. Dale, Feb 12 2015 *)

{ default(realprecision, 100); for (n=0, 1000, write("b062108.txt", n, " ", floor(n^(3/4) + 0.0000001)) ) } \\ Harry J. Smith, Aug 01 2009

a(n) = A061054(n) - n.

A134917 a(n) = ceiling(n^(4/3)).

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 14, 16, 19, 22, 25, 28, 31, 34, 37, 41, 44, 48, 51, 55, 58, 62, 66, 70, 74, 78, 81, 86, 90, 94, 98, 102, 106, 111, 115, 119, 124, 128, 133, 137, 142, 146, 151, 156, 161, 165, 170, 175, 180, 185, 190, 195, 200

Offset: 1

Mohammad K. Azarian, Nov 17 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A048766, A038605, A003059, A134914, A129011, A100196, A121536.

[Ceiling(n^(4/3)): n in [1..60]]; // Vincenzo Librandi, Feb 18 2013

Table[Ceiling[n^(4/3)], {n, 60}] (* Vincenzo Librandi, Feb 18 2013 *)

A134918 Ceiling(n^(5/3)).

Original entry on oeis.org

1, 4, 7, 11, 15, 20, 26, 32, 39, 47, 55, 63, 72, 82, 92, 102, 113, 124, 136, 148, 160, 173, 187, 200, 214, 229, 243, 259, 274, 290, 306, 323, 340, 357, 375, 393, 411, 430, 449, 468, 488, 508, 528, 549, 570, 591, 613, 634, 657

Offset: 1

Mohammad K. Azarian, Nov 17 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A048766, A038605, A003059, A134914, A129011, A100196, A121536, A134917.

[Ceiling(n^(5/3)): n in [1..50]]; // Vincenzo Librandi, Feb 18 2013

Table[Ceiling[n^(5/3)], {n, 50}] (* Vincenzo Librandi, Feb 18 2013 *)

A134919 Floor(n^(5/3)).

Original entry on oeis.org

1, 3, 6, 10, 14, 19, 25, 32, 38, 46, 54, 62, 71, 81, 91, 101, 112, 123, 135, 147, 159, 172, 186, 199, 213, 228, 243, 258, 273, 289, 305, 322, 339, 356, 374, 392, 410, 429, 448, 467, 487, 507, 527, 548, 569, 590, 612, 633, 656

Offset: 1

Mohammad K. Azarian, Nov 17 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A048766, A038605, A003059, A134914, A129011, A100196, A121536, A134917, A134918.

[Floor(n^(5/3)): n in [1..50]]; // Vincenzo Librandi, Feb 18 2013

Table[Floor[n^(5/3)], {n, 50}] (* Vincenzo Librandi, Feb 18 2013 *)

A079633 a(n) = floor(n/floor(n^(1/3))) - floor(n^(2/3)).

Original entry on oeis.org

0, 1, 1, 2, 3, 3, 4, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 5, 5, 4, 5, 5, 5, 6, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 4, 4

Offset: 1

Benoit Cloitre, Jan 30 2003

nonn

Cf. A048766, A100196.

a(n)=floor(n/sqrtnint(n,3))-sqrtnint(n^2,3)

For n > 4: Max_{k=1..n} a(k) = ceiling((n+2)^(1/3)) + 1.

cp's OEIS Frontend

A077106 Largest integer cube <= n^2.

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A032514 Sum of the integer part of 3/2-th roots of integers less than n.

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A077113 Number of nonnegative integer cubes <= n^2.

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A121536 Smallest m such that m^3 >= n^2.

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A062108 a(n) = floor(n^(3/4)).

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A134917 a(n) = ceiling(n^(4/3)).

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A134918 Ceiling(n^(5/3)).

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A134919 Floor(n^(5/3)).

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