A017979 -id:A017979 - cp's OEIS frontend

A018045 Powers of cube root of 24 rounded down.

1, 2, 8, 24, 69, 199, 576, 1661, 4792, 13824, 39875, 115020, 331776, 957007, 2760487, 7962624, 22968182, 66251701, 191102976, 551236370, 1590040835, 4586471424, 13229672880, 38160980055, 110075314176, 317512149143, 915863521339, 2641807540224, 7620291579445

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. powers of cube root of k rounded down: A017979 (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), A017991 (k=6), A017994 (k=7), A018000 (k=9), A018003 (k=10), A018006 (k=11), A018009 (k=12), A018012 (k=13), A018015 (k=14), A018018 (k=15), A018021 (k=16), A018024 (k=17), A018027 (k=18), A018030 (k=19), A018033 (k=20), A018036 (k=21), A018039 (k=22), A018042 (k=23), this sequence (k=24).

[Floor(24^(n/3)): n in [0..40]]; // Vincenzo Librandi, Jan 07 2014

Table[Floor[24^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 07 2014 *)
Floor[Surd[24,3]^Range[0,30]] (* Harvey P. Dale, Sep 14 2019 *)

More terms from Vincenzo Librandi, Jan 07 2014

A060969 Number of cubes of primes <= 2^n.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 8, 9, 11, 12, 15, 18, 22, 26, 31, 37, 46, 54, 66, 79, 97, 117, 141, 172, 209, 257, 309, 376, 457, 564, 687, 842, 1028, 1266, 1549, 1900, 2327, 2861, 3512, 4323, 5320, 6542, 8072, 9936, 12251, 15104, 18640, 23000, 28428

Offset: 0

Labos Elemer, May 09 2001

nonn

			For n = 10, the cubes of primes not exceeding 2^10 = 1024 are 8, 27, 125, 343, so a(10) = 4.

Cf. A000720, A007053, A017979, A030078, A036386, A060967, A060970, A060971.

Table[ PrimePi[ Floor[ 2^(g/3)//N ] ], {g, 0, 90} ]

a(3*n) = A007053(n). - Chai Wah Wu, Jan 23 2025

a(n) = A000720(A017979(n)). - Amiram Eldar, Mar 22 2025

Missing a(0)=0 inserted by Sean A. Irvine, Jan 09 2023

A018048 Powers of fourth root of 2 rounded down.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 8, 9, 11, 13, 16, 19, 22, 26, 32, 38, 45, 53, 64, 76, 90, 107, 128, 152, 181, 215, 256, 304, 362, 430, 512, 608, 724, 861, 1024, 1217, 1448, 1722, 2048, 2435, 2896, 3444, 4096, 4870, 5792, 6888, 8192, 9741, 11585, 13777, 16384

Offset: 0

N. J. A. Sloane

Matthew House, Table of n, a(n) for n = 0..10000

Cf. A017910, A017979, A018117.

seq(floor(2^(n/4)),n=0..100); #  Robert Israel, Jul 28 2015

a[n_] := Floor[2^(n/4)]; Array[a, 100, 0] (* Amiram Eldar, Apr 04 2025 *)

vector(70, n, n--; floor(2^(n/4))) \\ Michel Marcus, Jul 28 2015

a(n)=sqrtnint(2^n,4) \\ Charles R Greathouse IV, Jul 28 2015

A018117 Powers of fifth root of 2 rounded down.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 8, 9, 10, 12, 13, 16, 18, 21, 24, 27, 32, 36, 42, 48, 55, 64, 73, 84, 97, 111, 128, 147, 168, 194, 222, 256, 294, 337, 388, 445, 512, 588, 675, 776, 891, 1024, 1176, 1351, 1552, 1782, 2048, 2352, 2702, 3104, 3565, 4096

Offset: 0

N. J. A. Sloane

Amiram Eldar, Table of n, a(n) for n = 0..1000

Cf. A017910, A017979, A018048.

a[n_] := Floor[2^(n/5)]; Array[a, 100, 0] (* Amiram Eldar, Apr 04 2025 *)

a(n) = sqrtnint(2^n, 5) \\ Amiram Eldar, Apr 04 2025

A301370 Maximum determinant of an n X n (0,1)-matrix that has exactly 2*n ones.

Original entry on oeis.org

0, 2, 2, 3, 4, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64

Offset: 2

Hugo Pfoertner, Mar 20 2018

A proved upper bound is abs(a(n)) <= 6^(n/6), provided by Bruhn and Rautenbach. A conjectured sharper bound is abs(a(n)) <= 2^(n/3), provided by the same authors. For n=3*k, the bound is achieved by diagonally concatenating blocks ((1 1 0)(0 1 1)(1 0 1)).

The sharper bound is proved by Araujo, Balogh, and Wang in their article. See link. - Hugo Pfoertner, Nov 04 2020

			a(8) = 6 because no (0,1)-matrix with 2*8 ones with a greater determinant exists than
  ( 1 0 0 0 0 0 0 0 )
  ( 0 1 0 1 0 0 0 0 )
  ( 0 0 1 0 1 1 0 0 )
  ( 0 0 0 1 0 0 1 0 )
  ( 0 0 0 0 1 0 0 1 )
  ( 0 0 0 0 0 1 0 1 )
  ( 0 1 0 0 0 0 1 0 )
  ( 0 0 1 0 0 0 0 1 )

Igor Araujo, József Balogh, and Yuzhou Wang, Maximum determinant and permanent of sparse 0-1 matrices, arXiv:2011.01892 [math.CO], 3 Nov 2020.
Henning Bruhn and Dieter Rautenbach, Maximal determinants of combinatorial matrices, arXiv:1711.09935 [math.CO], 2017.
Mathoverflow, Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?, 2014-2018.
Yaroslav Shitov, On the determinant of a sparse 0-1 matrix, Linear Algebra and its Applications, Volume 554, 1 October 2018, Pages 49-50.
Markus Sigg, Gasper's determinant theorem, revisited, arXiv:1804.02897 [math.CO], 2018.

Cf. A003432, A017979, A085000.

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A018045 Powers of cube root of 24 rounded down.

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Magma

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A060969 Number of cubes of primes <= 2^n.

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A018048 Powers of fourth root of 2 rounded down.

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A018117 Powers of fifth root of 2 rounded down.

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A301370 Maximum determinant of an n X n (0,1)-matrix that has exactly 2*n ones.

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