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 10 results.

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

Original entry on oeis.org

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

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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.

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.

A132652 Sum of divisors of n, sigma(n) raised to power sigma(n).

Original entry on oeis.org

1, 27, 256, 823543, 46656, 8916100448256, 16777216, 437893890380859375, 302875106592253, 39346408075296537575424, 8916100448256, 33145523113253374862572728253364605812736, 11112006825558016, 1333735776850284124449081472843776
Offset: 1

Views

Author

Omar E. Pol, Aug 29 2007

Keywords

Examples

			a(4) = 823543 because sigma(4) = 1 + 2 + 4 = 7 and we can write 823543 = 7^7 or 823543 = 7*7*7*7*7*7*7.

Crossrefs

Cf. A000203 (sum of divisors: sigma function), A000312, A008973, A008974, A051674.

Programs

  • Mathematica
    Table[DivisorSigma[1,n]^DivisorSigma[1,n],{n,14}] (* Stefano Spezia, Sep 10 2022 *)

Formula

a(n) = sigma(n)^sigma(n).

A132653 Isolated prime I(n) raised to power I(n).

Original entry on oeis.org

4, 20880467999847912034355032910567, 10555134955777783414078330085995832946127396083370199442517, 3877924263464448622666648186154330754898344901344205917642325627886496385062863
Offset: 1

Views

Author

Omar E. Pol, Sep 01 2007

Keywords

Comments

Isolated primes: A007510. See T. D. Noe's table of n^n in the entry A000312.

Examples

			a(1)=4 because I(1)=2 and we can write 4=2^2 or 4=2*2.

Crossrefs

Cf. A000312, A007510, A008973, A008974, A051674.

Formula

a(n) = I(n)^I(n).

A132655 Pentagonal number P(n) raised to power P(n), for P(n) > 0.

Original entry on oeis.org

1, 3125, 8916100448256, 341427877364219557396646723584, 1102507499354148695951786433413508348166942596435546875
Offset: 1

Views

Author

Omar E. Pol, Aug 29 2007

Keywords

Comments

Pentagonal numbers: A000326.

Crossrefs

Cf. A000312, A000326, A008974.

A132656 Motzkin number M(n) raised to power M(n).

Original entry on oeis.org

1, 1, 4, 256, 387420489, 5842587018385982521381124421, 1219211305094648479473193481872927834667576992593770717189298225284399541977208231315051
Offset: 0

Views

Author

Omar E. Pol, Sep 07 2007

Keywords

Crossrefs

Motzkin numbers: A001006. Cf. A000312, A008973, A008974, A132639.
Showing 1-10 of 10 results.

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