A014058 -id:A014058 - cp's OEIS frontend

A014052 a(n) = floor((n+1/n)^n).

2, 6, 37, 326, 3802, 54992, 948645, 18992710, 432655358, 11046221254, 312347907386, 9688154906657, 327018557066164, 11932588574197763, 468012768020438830, 19634066192684343922, 877272066059957914873, 41590621075366029857195, 2085184183314142201403129

Offset: 1

N. J. A. Sloane, Jun 14 1998

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

Cf. A014056, A014058.

[Floor((n+1/n)^n): n in [1..20]]; // Vincenzo Librandi, Oct 17 2011

A014052:=n->floor((n+1/n)^n): seq(A014052(n), n=1..20); # Wesley Ivan Hurt, Aug 15 2016

Table[Floor[(n+1/n)^n], {n, 20}] (* Wesley Ivan Hurt, Aug 15 2016 *)

a(n)=(n+1/n)^n\1 \\ Charles R Greathouse IV, Apr 17 2012

[int((n+1/n)^n) for n in range(1,51)] # G. C. Greubel, Feb 05 2024

A014056 a(n) = round( (n + 1/n)^n ).

Original entry on oeis.org

2, 6, 37, 326, 3802, 54992, 948645, 18992711, 432655358, 11046221254, 312347907386, 9688154906658, 327018557066165, 11932588574197763, 468012768020438830, 19634066192684343923, 877272066059957914874

Offset: 1

N. J. A. Sloane

nonn

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

Cf. A014052, A014058.

[Round((n+1/n)^n): n in [1..20]]; // Vincenzo Librandi, Oct 20 2011

Table[Round[(n+1/n)^n], {n,50}] (* G. C. Greubel, Feb 05 2024 *)

a(n)=round((n+1/n)^n) \\ Charles R Greathouse IV, Jul 01 2013

[round((n+1/n)^n) for n in range(1,51)] # G. C. Greubel, Feb 05 2024

A197716 a(n) = ceiling((2n+1/n)^n).

Original entry on oeis.org

3, 21, 255, 4633, 110409, 3243618, 113177497, 4570858600, 209655304353, 10763674952098, 611433842280388, 38071427445729201, 2578294348444597267, 188670154792420320215, 14834716200104606205408, 1247263229999781126495328, 111661618863544248806155260

Offset: 1

Vincenzo Librandi, Oct 18 2011

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

Cf. A014058.

Magma
```
[Ceiling((2*n+1/n)^n): n in [1..20]]
```

Array[Ceiling[(2*# + 1/#)^#] &, 20] (* Paolo Xausa, Feb 04 2025 *)

a(n)=ceil((2*n+1/n)^n) \\ Charles R Greathouse IV, Nov 21 2011

A197717 a(n) = ceiling((3n+1/n)^n).

Original entry on oeis.org

4, 43, 814, 22519, 811369, 35946076, 1888624972, 114746269758, 7912720985080, 610470884770407, 52094956940751711, 4871691779130290167, 495409898474358881327, 54427906182810588386674, 6424384909407981686846706, 810777549111969648699638307, 108944087230453697240059783284

Offset: 1

Vincenzo Librandi, Oct 18 2011

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

Cf. A014058.

Magma
```
[Ceiling((3*n+1/n)^n): n in [1..20]]
```

Table[Ceiling[(3n+1/n)^n],{n,20}] (* Harvey P. Dale, Mar 04 2023 *)

a(n)=ceil((3*n+1/n)^n) \\ Charles R Greathouse IV, Nov 21 2011

A197764 Ceiling((4n+1/n)^n).

Original entry on oeis.org

5, 73, 1877, 69730, 3363233, 199205127, 13982257729, 1134344816185, 104416147080712, 10750872867074587, 1224163955433850944, 152733676280699540999, 20719969553916698313305, 3036565789908881887393114, 478082645334119488823777215, 80475210949356295594385157621

Offset: 1

Vincenzo Librandi, Oct 18 2011

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

Cf. A014058.

Magma
```
[Ceiling((4*n+1/n)^n): n in [1..20]]
```

a(n)=ceil((4*n+1/n)^n) \\ Charles R Greathouse IV, Nov 21 2011

A197765 a(n) = ceiling((5n+1/n)^n).

Original entry on oeis.org

6, 111, 3606, 168152, 10162551, 753640011, 66200225627, 6719243243860, 773662803646265, 99627047203913815, 14186632841753756406, 2213340465298424454703, 375449162169269152689332, 68797650004483898373052061, 13542753444466024362689788809

Offset: 1

Vincenzo Librandi, Oct 18 2011

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

Cf. A014058.

Magma
```
[Ceiling((5*n+1/n)^n): n in [1..20]]
```

Table[Ceiling[(5n+1/n)^n],{n,20}] (* Harvey P. Dale, Nov 16 2021 *)

a(n)=ceil((5*n+1/n)^n) \\ Charles R Greathouse IV, Nov 21 2011

A197766 Ceiling((6n+1/n)^n).

Original entry on oeis.org

7, 157, 6163, 345818, 25120873, 2237952688, 236084694123, 28771727614750, 3977205817386553, 614815375624938277, 105089416995538138498, 19679693805738843682351, 4006775128162674717660622, 881207085092349552894218730, 208190711541113653367733416164

Offset: 1

Vincenzo Librandi, Oct 18 2011

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

Cf. A014058.

Magma
```
[Ceiling((6*n+1/n)^n): n in [1..20]]
```

Table[Ceiling[(6n+1/n)^n],{n,20}] (* Harvey P. Dale, Jun 06 2020 *)

a(n)=ceil((6*n+1/n)^n) \\ Charles R Greathouse IV, Nov 21 2011

A197910 Ceiling((n+1/2)^n).

Original entry on oeis.org

2, 7, 43, 411, 5033, 75419, 1334839, 27249053, 630249410, 16288946268, 465239139607, 14551915228367, 494696673952512, 18161513224841276, 716102966059713316, 30181658957863752410, 1354087807629298185930, 64430442087414935111822, 3240840189607299761533536

Offset: 1

Vincenzo Librandi, Oct 19 2011

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

Cf. A014058.

Magma
```
[Ceiling((n+1/2)^n): n in [1..20]]
```

Table[Ceiling[(n+1/2)^n],{n,20}] (* Harvey P. Dale, Sep 05 2015 *)

a(n)=ceil((n+1/2)^n) \\ Charles R Greathouse IV, Nov 21 2011

A197904 a(n) = ceiling((n+1/n)^5).

Original entry on oeis.org

32, 98, 412, 1387, 3803, 8918, 18594, 35410, 62786, 105102, 167817, 257593, 382409, 551685, 776401, 1069217, 1444593, 1918909, 2510585, 3240201, 4130617, 5207093, 6497409, 8031985, 9844001, 11969517, 14447593, 17320409, 20633385, 24435301, 28778417, 33718593

Offset: 1

Vincenzo Librandi, Oct 19 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A014058.

Magma
```
[Ceiling((n+1/n)^5): n in [1..50]]
```

A197904:=n->ceil((n+1/n)^5): seq(A197904(n), n=1..40); # Wesley Ivan Hurt, Apr 23 2017

Table[Ceiling[(n+1/n)^5],{n,50}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{32,98,412,1387,3803,8918,18594,35410,62786,105102,167817,257593,382409,551685,776401,1069217},40] (* Harvey P. Dale, Jul 10 2021 *)

a(n)=ceil((n+1/n)^5) \\ Charles R Greathouse IV, Nov 21 2011

a(n) = n^5 + 5n^3 + 10n for n > 10. [Charles R Greathouse IV, Nov 21 2011]
G.f.: (167817 - 749309 x + 1354106 x^2 - 1235214 x^3 + 567821 x^4 -
105101 x^5)/(-1 + x)^6 - Harvey P. Dale, Jul 10 2021

A197907 Ceiling((n+1/n)^8).

Original entry on oeis.org

256, 1526, 15242, 106442, 534598, 2091240, 6776037, 18992711, 47486564, 108285671, 228948164, 454458311, 855154436, 1537112039, 2655445796, 4431034439, 7171212836, 11295015911, 17363599364, 26116502471, 38514458564, 55789499111, 79503137636, 111613460039

Offset: 1

Vincenzo Librandi, Oct 19 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A014058.

Magma
```
[Ceiling((n+1/n)^8): n in [1..40]]
```

Table[Ceiling[(n+1/n)^8],{n,30}] (* Harvey P. Dale, Jul 10 2013 *)

a(n)=ceil((n+1/n)^8) \\ Charles R Greathouse IV, Dec 27 2011

For n > 7, a(n) = n^8 + 8n^6 + 28n^4 + 56n^2 + 70. [Charles R Greathouse IV, Dec 27 2011]

cp's OEIS Frontend

A014052 a(n) = floor((n+1/n)^n).

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A014056 a(n) = round( (n + 1/n)^n ).

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A197716 a(n) = ceiling((2n+1/n)^n).

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A197717 a(n) = ceiling((3n+1/n)^n).

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A197764 Ceiling((4n+1/n)^n).

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A197765 a(n) = ceiling((5n+1/n)^n).

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Magma

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A197766 Ceiling((6n+1/n)^n).

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Magma

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PARI

A197910 Ceiling((n+1/2)^n).

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