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.

Showing 1-10 of 13 results. Next

A250495 The n^n-th Fibonacci number.

Original entry on oeis.org

1, 1, 3, 196418, 141693817714056513234709965875411919657707794958199867
Offset: 0

Views

Author

Alois P. Heinz, Nov 24 2014

Keywords

Comments

The next term (a(5)) has 653 digits. - Harvey P. Dale, Nov 29 2017

Links

Crossrefs

Cf. A000045, A000312, A008973, A250486.

Programs

  • Maple
    a:= n-> (<<0|1>, <1|1>>^(n^n))[1, 2]:
seq(a(n), n=0..5);
  • Mathematica
    Table[Fibonacci[n^n],{n,0, 5}] (* Harvey P. Dale, Nov 29 2017 *)

Formula

a(n) = [0, 1; 1, 1]^(n^n)[1,2].
a(n) = A000045(n^n) = A250486(n,n).
a(n) = A000045(A000312(n)).

A090242 a(n) = F(n)^F(n-1), where F is the Fibonacci sequence A000045.

Original entry on oeis.org

0, 1, 1, 2, 9, 125, 32768, 815730721, 154472377739119461, 144896287389534090178492559785984, 148707010444932320126692907511838968493975698947906494140625, 164607782908174441344270105333730757465593941470198419854718194253607242940724175602015628380155976898641449
Offset: 0

Views

Author

Felix Tubiana, Jan 23 2004

Keywords

Examples

			a(5) = 5^3 = 125.

Crossrefs

Cf. A000045, A008973, A090241.

Programs

  • Mathematica
    Last[#]^First[#]&/@Partition[Fibonacci[Range[-1,12]],2,1]  (* Harvey P. Dale, Apr 16 2011 *)

Extensions

Edited by N. J. A. Sloane, Sep 19 2007

A132637 Composite number C(n) raised to power C(n).

Original entry on oeis.org

256, 46656, 16777216, 387420489, 10000000000, 8916100448256, 11112006825558016, 437893890380859375, 18446744073709551616, 39346408075296537575424, 104857600000000000000000000, 5842587018385982521381124421, 341427877364219557396646723584
Offset: 1

Views

Author

Omar E. Pol, Aug 24 2007

Keywords

Crossrefs

Cf. A002808, A008973, A051674, A062312, A085534, A094724, A106575.

Programs

  • Mathematica
    With[{nn=25},#^#&/@Complement[Range[2,nn],Prime[Range[PrimePi[nn]]]]] (* Harvey P. Dale, Aug 21 2011 *)

Formula

From Amiram Eldar, Nov 18 2020: (Start)
a(n) = A002808(n)^A002808(n).
1 + Sum_{n>=1} 1/a(n) = A094724. (End)

Extensions

More terms from Harvey P. Dale, Aug 21 2011

A132639 Catalan number C(n) raised to power C(n).

Original entry on oeis.org

1, 1, 4, 3125, 11112006825558016
Offset: 1

Views

Author

Omar E. Pol, Aug 24 2007

Keywords

Examples

			a(4)=3125 because C(4)=5 and we can write 3125=5^5 or 3125=5*5*5*5*5.

Crossrefs

Cf. A000108, A008973, A008974, A051674.

Formula

a(n) = (C(n))^(C(n)).

A132641 Number of partitions of n, p(n), raised to power p(n).

Original entry on oeis.org

1, 1, 4, 27, 3125, 823543, 285311670611, 437893890380859375, 341427877364219557396646723584, 205891132094649000000000000000000000000000000, 150130937545296572356771972164254457814047970568738777235893533016064
Offset: 0

Views

Author

Omar E. Pol, Aug 24 2007

Keywords

Comments

a(n) is also the number of endofunctions on the partitions of n. - Max Sills, Feb 07 2012

Examples

			a(5) = 823543 because p(5) = 7 and we can write 823543 = 7^7 or 823543 = 7*7*7*7*7*7*7.

Crossrefs

Cf. A000041, A000312, A008973, A008974, A051674.

Programs

  • Maple
    a:= n-> (p-> p^p)(combinat[numbpart](n)):
seq(a(n), n=0..11);  # Alois P. Heinz, Nov 04 2024
  • Mathematica
    Table[ PartitionsP@n ^ PartitionsP@n, {n, 10}] (* Robert G. Wilson v, Aug 28 2007 *)

Formula

a(n) = p(n)^p(n).
a(n) = A000312(A000041(n)). - Alois P. Heinz, Nov 04 2024

Extensions

More terms from Robert G. Wilson v, Aug 28 2007
a(0)=1 prepended by Alois P. Heinz, Nov 04 2024

A132650 a(n) = d(n)^d(n), where d(n) = A000005(n).

Original entry on oeis.org

1, 4, 4, 27, 4, 256, 4, 256, 27, 256, 4, 46656, 4, 256, 256, 3125, 4, 46656, 4, 46656, 256, 256, 4, 16777216, 27, 256, 256, 46656, 4, 16777216, 4, 46656, 256, 256, 256, 387420489, 4, 256, 256, 16777216, 4, 16777216, 4, 46656, 46656, 256, 4, 10000000000, 27, 46656
Offset: 1

Views

Author

Omar E. Pol, Aug 29 2007

Keywords

Examples

			a(12) = 46656 because d(12) = 6 and we can write 46656 = 6^6 or 46656.

Links

Crossrefs

Cf. A000005, A008973, A008974, A051674.

Programs

  • Mathematica
    Table[dn=DivisorSigma[0,n];dn^dn,{n,50}] (* James C. McMahon, Mar 08 2025 *)

Formula

a(n) = d(n)^d(n), where d(n) = A000005(n).

Extensions

a(48)-a(50) from James C. McMahon, Mar 08 2025

A132638 Numbers of the form m^m where m is oblong (promic).

Original entry on oeis.org

4, 46656, 8916100448256, 104857600000000000000000000, 205891132094649000000000000000000000000000000, 150130937545296572356771972164254457814047970568738777235893533016064
Offset: 1

Views

Author

Omar E. Pol, Aug 24 2007

Keywords

Examples

			a(2)=46656 because we can write 46656=6^6 or 46656=6*6*6*6*6*6.

Crossrefs

Subsequence of A000312.
Oblong numbers: A002378
Cf. A008973, A008974, A051674.

Programs

Formula

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

Extensions

New name and a(5)-a(6) from Charles R Greathouse IV, Mar 16 2022

A132640 Number of trees with n unlabeled nodes T(n) raised to power T(n).

Original entry on oeis.org

1, 1, 1, 4, 27, 46656, 285311670611, 20880467999847912034355032910567, 3877924263464448622666648186154330754898344901344205917642325627886496385062863
Offset: 1

Views

Author

Omar E. Pol, Aug 24 2007

Keywords

Crossrefs

Number of trees with n unlabeled nodes: A000055.
Cf. A008973, A008974, A051674.

A132649 Lucky number L(n) raised to power L(n).

Original entry on oeis.org

1, 27, 823543, 387420489, 302875106592253, 437893890380859375, 5842587018385982521381124421
Offset: 1

Views

Author

Omar E. Pol, Aug 27 2007

Keywords

Comments

Lucky numbers: A000959.

Crossrefs

Cf. A000959, A008973.

Formula

a(n)=L(n)^L(n).

A132651 Sum of proper divisors of n, s(n) raised to power s(n), for n > 1.

Original entry on oeis.org

1, 1, 27, 1, 46656, 1, 823543, 256, 16777216, 1, 18446744073709551616, 1, 10000000000, 387420489, 437893890380859375, 1, 5842587018385982521381124421, 1, 341427877364219557396646723584
Offset: 2

Views

Author

Omar E. Pol, Aug 29 2007

Keywords

Comments

Sum of proper divisors of n: A001065.

Crossrefs

Cf. A000005, A000040, A000312, A001065, A008973, A008974, A051674.
Showing 1-10 of 13 results. Next

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

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