cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-18 of 18 results.

A051443 a(n) = n^(n+1)*(n+1)^n.

Original entry on oeis.org

0, 2, 72, 5184, 640000, 121500000, 32934190464, 12089663946752, 5777633090469888, 3486784401000000000, 2593742460100000000000, 2331878554708454877954048, 2492736806448711465154117632, 3125153805191532199063557103616, 4541487905530112153400000000000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A007925, A051442.

Programs

A174379 a(n) is the largest prime factor of (n-1)^n - n^(n-1).

Original entry on oeis.org

17, 19, 167, 162287, 159463, 354751, 2486784401, 12589253, 71549927, 83695120256591, 556123, 10902870290089, 25793, 362561, 26757560905578361, 6015993258685545623, 55044966589, 1182622403647894934149, 9973660056412561, 38783069052902219, 4576344458074395243073
Offset: 4

Views

Author

Torbjorn Alm (talm(AT)tele2.se), Mar 17 2010

Keywords

Comments

A007925(n) = (n-1)^n - n^(n-1).
A007925(n) = -1 for n = 1..3, which has no prime factors, so the offset is 4.

Examples

			19 is a term because 4^5 - 5^4 = 399 = 19 * 21. - _Bernard Schott_, Jan 14 2019

Links

Crossrefs

Cf. A007925.

Programs

  • Magma
    [Maximum(PrimeDivisors((n-1)^n - n^(n-1))): n in [4..25]]; // Vincenzo Librandi, Jan 14 2019
  • Mathematica
    Table[FactorInteger[(n - 1)^n - n^(n - 1)][[-1, 1]], {n, 4, 20}] (* Vincenzo Librandi, Jan 14 2019 *)
  • PARI
    a(n) = vecmax(factor((n-1)^n - n^(n-1))[,1]);
for (n=4, 30, print1(a(n), ", ")) \\ Michel Marcus, Jan 14 2019

Extensions

a(4) corrected, a(22)-a(24) added, and other edits by Jon E. Schoenfield, Jan 13 2019

A058124 n^(n^n)-(n^n)^n with 0^0=1.

Original entry on oeis.org

-1, 0, 0, 7625597465304
Offset: 0

Views

Author

Henry Bottomley, Nov 10 2000

Keywords

Examples

			a(2)=2^4-4^2=16-16=0. a(3)=3^27-27^3=7625597484987-19683=7625597465304

Links

Crossrefs

Cf. A002488, A002489, A007925, A058125.

Formula

a(n) =A002488(n)-A002489(n)

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 24 2011

A111454 a(n) = (n-4)^(n-3) - (n-3)^(n-4) + 1.

Original entry on oeis.org

0, 0, 0, 18, 400, 7850, 162288, 3667650, 91171008, 2486784402, 74062575400, 2395420006034, 83695120256592, 3143661612445146, 126375169532421600, 5415486851106043650, 246486713303685957376
Offset: 4

Views

Author

Robert J. Reid (greencroft57(AT)yahoo.co.uk), Nov 14 2005

Keywords

Links

Crossrefs

Cf. A007925.

Programs

  • Mathematica
    Table[(n-4)^(n-3)-(n-3)^(n-4)+1,{n,4,20}] (* Harvey P. Dale, Oct 05 2019 *)

Formula

a(n) = A007925(n-4) + 1. - Mathew Englander, Aug 14 2020

Extensions

More terms from R. J. Mathar, Feb 26 2008

A155539 a(n) = n^(n+3) + (n+3)^n.

Original entry on oeis.org

1, 5, 57, 945, 18785, 423393, 10609137, 292475249, 8804293473, 287589316833, 10137858491849, 383799398752905, 15536767912476993, 669920208810550337, 30659724555890596833, 1484638520651877849057, 75846305139481944586817
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 23 2009

Keywords

Comments

1^4 + 4^1 = 5, 2^5 + 5^2 = 57, ...

Links

Crossrefs

Cf. A046065, A051442, A007925, A051489, A153217, A076980.

Programs

  • Magma
    [n^(n+3)+(n+3)^n: n in [0..20] ]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    lst={};Do[m=n+3;q=n^m+m^n;AppendTo[lst,q],{n,0,4!}];lst
Table[n^(n+3)+(n+3)^n,{n,0,20}] (* Harvey P. Dale, Aug 18 2024 *)

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 24 2011

A062276 a(n) = floor(n^(n+1) / (n+1)^n).

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28
Offset: 0

Views

Author

Henry Bottomley, Jul 02 2001

Keywords

Comments

a(n) is close to n/e (cf. A032634).

Examples

			a(2) = floor(2^3/3^2) = floor(8/9) = 0.

Links

Crossrefs

Cf. A032634. Cf. A000169, A007778, A007925.

Programs

  • GAP
    List([0..90],n->Int(n^(n+1)/(n+1)^n)); # Muniru A Asiru, Jul 01 2018
  • Maple
    seq(floor(n^(n+1)/(n+1)^n),n=0..90); # Muniru A Asiru, Jul 01 2018
  • Mathematica
    Array[Floor[#^(# + 1)/(# + 1)^#] &, 78, 0] (* Michael De Vlieger, Jul 01 2018 *)
  • PARI
    { default(realprecision, 50); for (n=0, 1000, write("b062276.txt", n, " ", floor(n^(n + 1) / (n + 1)^n)) ) } \\ Harry J. Smith, Aug 03 2009

A166326 a(n) = prime(n)^(prime(n)+1) - (prime(n)+1)^prime(n).

Original entry on oeis.org

-1, 17, 7849, 3667649, 2395420006033, 3143661612445145, 11877172892329028459041, 32347093457545958193355601, 424678439961073471604787362241217
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Oct 11 2009

Keywords

Examples

			a(1) = 2^3 - 3^2 = -1. a(2) = 3^4 - 4^3 = 17. a(3) = 5^6 - 6^5 = 7849.

Crossrefs

Cf. A000040, A007925, A140893, A104126, A104127.

Programs

  • Mathematica
    Array[Prime[ # ]^(Prime[ # ]+1)-(Prime[ # ]+1)^Prime[ # ]&,16]

Formula

a(n) = A104126(n) - A104127(n) = A007925(A000040(n)). - R. J. Mathar, Oct 14 2009

Extensions

Keyword:sign set by R. J. Mathar, Oct 14 2009

A094647 a(n) = n^(2n) - (2n)^n.

Original entry on oeis.org

-1, 0, 513, 61440, 9665625, 2173796352, 678117659345, 281470681743360, 150094436937708753, 99999989760000000000, 81402748802521459701993, 79496847166870496697384960, 91733330190787463785195879433
Offset: 1

Views

Author

Gregory S. Thoman (fealuinix(AT)yahoo.com), May 18 2004

Keywords

Examples

			a(3) = 513 because 3^(2*3) - (2*3)^3 = 3^6 - 6^3 = 513.

Crossrefs

Cf. A007925, A046065.

Programs

  • Mathematica
    a[n_] := n^n(n^n - 2^n); Table[a[n], {n, 13}] (* Robert G. Wilson v, May 24 2004 *)

Extensions

More terms from Emeric Deutsch, Robert G. Wilson v and Pab Ter (pabrlos(AT)yahoo.com), May 24 2004
Previous Showing 11-18 of 18 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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