A053638 -id:A053638 - cp's OEIS frontend

A000799 a(n) = floor(2^n / n).

2, 2, 2, 4, 6, 10, 18, 32, 56, 102, 186, 341, 630, 1170, 2184, 4096, 7710, 14563, 27594, 52428, 99864, 190650, 364722, 699050, 1342177, 2581110, 4971026, 9586980, 18512790, 35791394, 69273666, 134217728, 260301048, 505290270, 981706810, 1908874353

Offset: 1

N. J. A. Sloane

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).

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A000801, A053638, A065482, A082482, A071354, A193359.

List([1..40],n->Int(2^n/n)); # Muniru A Asiru, Oct 20 2018

[2^n div n : n in [1..40]]; // Vincenzo Librandi, Oct 14 2018

seq(floor(2^n/n),n=1..40); # Muniru A Asiru, Oct 20 2018

Table[Quotient[2^n,n],{n,60}] (* Vladimir Joseph Stephan Orlovsky, May 07 2011 *)

PARI
```
a(n)=1<
				
```

for n in range(1, 40): print(int(2**n / n), end=", ") # Stefano Spezia, Oct 20 2018

Sum_{n>=1} 1/a(n) = A193359. - Amiram Eldar, Apr 03 2021

A082482 a(n) = floor of (2^n-1)/n.

Original entry on oeis.org

1, 1, 2, 3, 6, 10, 18, 31, 56, 102, 186, 341, 630, 1170, 2184, 4095, 7710, 14563, 27594, 52428, 99864, 190650, 364722, 699050, 1342177, 2581110, 4971026, 9586980, 18512790, 35791394, 69273666, 134217727, 260301048, 505290270, 981706810

Offset: 1

Jon Perry, Apr 27 2003

nonn

a(n) is the largest exponent k such that (2^n)^k || (2^n)!. - Lekraj Beedassy, Jan 15 2024

			a(3) = floor((2^3-1)/3) = floor(7/3) = floor(2.333) = 2.

Robert Israel, Table of n, a(n) for n = 1..3320

Cf. A023359, A082495, A162214.

a(n) = A053638(n) - 1.

seq(floor((2^n-1)/n), n=1..100); # Robert Israel, Dec 01 2016

for (n=1,50,print1(floor((2^n-1)/n)","))

a(n) = (2^n - 1 - A082495(n))/n = A162214(n)/n. - Robert Israel, Dec 01 2016

A129795 a(n) = floor(5^n/n).

Original entry on oeis.org

5, 12, 41, 156, 625, 2604, 11160, 48828, 217013, 976562, 4438920, 20345052, 93900240, 435965401, 2034505208, 9536743164, 44878791360, 211927625868, 1003867701480, 4768371582031, 22706531343005, 108372081409801

Offset: 1

Mohammad K. Azarian, May 18 2007

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A000799, A092763, A053638.

[Floor(5^n / n): n in [1..35]]; // Vincenzo Librandi, May 08 2011

Table[Floor[5^n/n],{n,30}] (* Harvey P. Dale, Jul 19 2011 *)

A082493 a(n) = n*ceiling(2^n/n) - 2^n.

Original entry on oeis.org

0, 0, 1, 0, 3, 2, 5, 0, 1, 6, 9, 8, 11, 10, 7, 0, 15, 8, 17, 4, 13, 18, 21, 8, 18, 22, 1, 12, 27, 26, 29, 0, 25, 30, 17, 8, 35, 34, 31, 24, 39, 20, 41, 28, 28, 42, 45, 32, 19, 26, 43, 36, 51, 26, 12, 24, 49, 54, 57, 44, 59, 58, 55, 0, 33, 2, 65, 52, 61, 26, 69, 8, 71, 70, 7, 60, 59, 14

Offset: 1

Vladeta Jovovic, Apr 28 2003

Least nonnegative k such that (2^n+k)/n is an integer.

If n is a power of 2, a(n) = 0; otherwise a(n) = n - A015910(n). - Robert Israel, Apr 08 2015

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A053638, A015910, A000799, A082494, A215747.

seq(-2&^n mod n, n = 1 .. 100); # Robert Israel, Apr 08 2015

def A082493(n): return (-pow(2,n,n))%n # Chai Wah Wu, Aug 24 2023

a(n) = -(2^n) mod n. - Robert Israel, Apr 08 2015

A129794 a(n) = floor(4^n/n).

Original entry on oeis.org

4, 8, 21, 64, 204, 682, 2340, 8192, 29127, 104857, 381300, 1398101, 5162220, 19173961, 71582788, 268435456, 1010580540, 3817748707, 14467258260, 54975581388, 209430786243, 799644820200, 3059510616420, 11728124029610

Offset: 1

Mohammad K. Azarian, May 18 2007

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A000799, A092763, A053638.

[Floor(4^n / n): n in [1..35]]; // Vincenzo Librandi, May 08 2011

Table[Floor[4^n/n],{n,25}] (* Harvey P. Dale, Jul 24 2011 *)

def A129794(n): return (1<<(n<<1))//n # Chai Wah Wu, Aug 24 2023

A129796 a(n) = floor(6^n/n).

Original entry on oeis.org

6, 18, 72, 324, 1555, 7776, 39990, 209952, 1119744, 6046617, 32981550, 181398528, 1004668770, 5597440292, 31345665638, 176319369216, 995685849690, 5642219814912, 32071565263710, 182807922003148, 1044616697160850

Offset: 1

Mohammad K. Azarian, May 18 2007

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A000799, A092763, A053638.

[Floor(6^n / n): n in [1..25]]; // Vincenzo Librandi, May 08 2011

Table[Floor[6^n/n],{n,30}] (* Harvey P. Dale, Feb 20 2015 *)

A129797 a(n) = floor(7^n/n).

Original entry on oeis.org

7, 24, 114, 600, 3361, 19608, 117649, 720600, 4483734, 28247524, 179756976, 1153440600, 7453000800, 48444505203, 316504100662, 2077058160600, 13684147881600, 90467422106136, 599941851861744, 3989613314880600

Offset: 1

Mohammad K. Azarian, May 18 2007

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A000799, A092763, A053638.

[Floor(7^n / n): n in [1..25]]; // Vincenzo Librandi, May 08 2011

Table[Floor[7^n/n],{n,30}] (* Harvey P. Dale, Dec 05 2012 *)

A129798 a(n) = floor(8^n/n).

Original entry on oeis.org

8, 32, 170, 1024, 6553, 43690, 299593, 2097152, 14913080, 107374182, 780903144, 5726623061, 42288908760, 314146179364, 2345624805922, 17592186044416, 132458812569720, 1000799917193443, 7585009898729256

Offset: 1

Mohammad K. Azarian, May 18 2007

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A000799, A092763, A053638.

[Floor(8^n / n): n in [1..25]]; // Vincenzo Librandi, May 08 2011

Table[Floor[8^n/n],{n,20}] (* Harvey P. Dale, Aug 03 2019 *)

A129799 a(n) = floor(9^n/n).

Original entry on oeis.org

9, 40, 243, 1640, 11809, 88573, 683281, 5380840, 43046721, 348678440, 2852823600, 23535794706, 195528140640, 1634056603925, 13726075472976, 115813761803240, 981010688215680, 8338590849833284, 71097458824894320

Offset: 1

Mohammad K. Azarian, May 18 2007

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A000799, A092763, A053638.

[Floor(9^n / n): n in [1..25]]; // Vincenzo Librandi, May 08 2011

A053639 a(n) = ceiling(2^(n+1)/n).

Original entry on oeis.org

4, 4, 6, 8, 13, 22, 37, 64, 114, 205, 373, 683, 1261, 2341, 4370, 8192, 15421, 29128, 55189, 104858, 199729, 381301, 729445, 1398102, 2684355, 5162221, 9942054, 19173962, 37025581, 71582789, 138547333, 268435456, 520602097

Offset: 1

N. J. A. Sloane, Mar 23 2000

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

Cf. A053637, A053638.

[Ceiling(2^(n+1)/n): n in [1..40]]; // Vincenzo Librandi, Dec 19 2011

A053639:=n->ceil(2^(n+1)/n): seq(A053639(n), n=1..40); # Wesley Ivan Hurt, Jan 19 2017

Table[Ceiling[2^(n+1)/n],{n,1,40}] (* Vincenzo Librandi, Dec 19 2011 *)

vector(40, n, ceil(2^(n+1)/n) ) \\ G. C. Greubel, May 17 2019

[ceil(2^(n+1)/n) for n in (1..40)] # G. C. Greubel, May 17 2019

cp's OEIS Frontend

A000799 a(n) = floor(2^n / n).

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A082482 a(n) = floor of (2^n-1)/n.

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A129795 a(n) = floor(5^n/n).

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Magma

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A082493 a(n) = n*ceiling(2^n/n) - 2^n.

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Maple

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Formula

A129794 a(n) = floor(4^n/n).

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Magma

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Python

A129796 a(n) = floor(6^n/n).

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Programs

Magma

Mathematica

A129797 a(n) = floor(7^n/n).

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Programs

Magma

Mathematica

A129798 a(n) = floor(8^n/n).

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