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 1-6 of 6 results.

A363829 Sum of the divisors of A000129(n) (Pell numbers).

Original entry on oeis.org

1, 3, 6, 28, 30, 144, 183, 1080, 1188, 3780, 5742, 52416, 33462, 131760, 251100, 1290096, 1145124, 5702400, 6804204, 42336000, 50176404, 146352096, 226041700, 2333111040, 1357893000, 4818528000, 9395060400, 47385112320, 44560482150, 251337038400, 264178169640
Offset: 1

Views

Author

Tyler Busby, Oct 19 2023

Keywords

Examples

			a(9)=1188 because Pell(9)=985 has divisors {1, 5, 197, 985}.

Links

Crossrefs

Cf. A000129, A000203, A272040, A363831, A363833, A364818, A364820.

Programs

  • Mathematica
    DivisorSigma[1, LinearRecurrence[{2, 1}, {1, 2}, 32]] (* Amiram Eldar, Oct 19 2023 *)

Formula

a(n) = sigma(Pell(n)) = A000203(A000129(n)).

A363831 Number of divisors of A000129(n) (Pell numbers).

Original entry on oeis.org

1, 2, 2, 6, 2, 8, 3, 16, 4, 8, 2, 72, 2, 12, 12, 40, 4, 32, 4, 96, 12, 16, 4, 384, 8, 16, 16, 144, 2, 288, 8, 96, 8, 32, 12, 1536, 8, 16, 16, 1024, 2, 288, 4, 384, 96, 32, 4, 3840, 12, 64, 32, 192, 2, 256, 32, 768, 32, 8, 2, 41472, 8, 64, 96, 896, 64, 256, 4
Offset: 1

Views

Author

Tyler Busby, Oct 19 2023

Keywords

Examples

			a(9)=4 because Pell(9)=985 has divisors {1, 5, 197, 985}.

Links

Crossrefs

Cf. A000005, A000129, A272040, A363829.

Programs

  • Mathematica
    DivisorSigma[0,LinearRecurrence[{2,1},{1,2},67]] (* Stefano Spezia, Oct 19 2023 *)

Formula

a(n) = sigma0(Pell(n)) = A000005(A000129(n)).

A364818 Number of distinct prime divisors of A000129(n) (Pell numbers).

Original entry on oeis.org

0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 5, 1, 3, 3, 4, 2, 5, 2, 6, 3, 4, 2, 7, 3, 4, 4, 6, 1, 7, 3, 5, 3, 5, 3, 9, 3, 4, 4, 9, 1, 7, 2, 8, 6, 5, 2, 10, 3, 6, 5, 7, 1, 8, 5, 8, 5, 3, 1, 13, 3, 6, 6, 8, 6, 8, 2, 9, 4, 8, 3, 13, 2, 7, 8, 9, 5, 10, 4, 12, 7, 5, 2, 14, 7
Offset: 1

Views

Author

Tyler Busby, Oct 21 2023

Keywords

Examples

			a(8)=3 because Pell(8)=408 has prime factors {2, 2, 2, 3, 17}.

Links

Crossrefs

Cf. A000129, A001221, A272040, A363829, A363831, A363833.

Programs

  • Mathematica
    PrimeNu[LinearRecurrence[{2, 1}, {1, 2}, 85]] (* Amiram Eldar, Oct 21 2023 *)

Formula

a(n) = omega(Pell(n)) = A001221(A000129(n)).

A363833 Number of prime factors of A000129(n) (Pell numbers) (counted with multiplicity).

Original entry on oeis.org

0, 1, 1, 3, 1, 3, 2, 5, 2, 3, 1, 7, 1, 4, 4, 7, 2, 5, 2, 7, 4, 4, 2, 10, 3, 4, 4, 8, 1, 9, 3, 9, 3, 5, 4, 12, 3, 4, 4, 11, 1, 9, 2, 9, 7, 5, 2, 14, 4, 6, 5, 8, 1, 8, 5, 11, 5, 3, 1, 17, 3, 6, 7, 13, 6, 8, 2, 10, 4, 9, 3, 17, 2, 7, 10, 10, 6, 10, 4, 15, 7, 5, 2
Offset: 1

Views

Author

Tyler Busby, Oct 19 2023

Keywords

Examples

			a(8)=5 because Pell(8)=408 has prime factors {2, 2, 2, 3, 17}.

Links

Crossrefs

Cf. A000129, A001222, A272040, A363829, A363831, A364818.

Programs

  • Mathematica
    PrimeOmega[LinearRecurrence[{2,1},{1,2},83]] (* Stefano Spezia, Oct 19 2023 *)

Formula

a(n) = bigomega(Pell(n)) = A001222(A000129(n)).

A107647 Euler's totient function applied to tribonacci numbers.

Original entry on oeis.org

1, 1, 1, 2, 6, 12, 8, 20, 54, 148, 136, 144, 612, 1200, 1344, 2448, 10506, 16848, 13824, 22000, 83232, 148716, 205368, 377736, 920160, 1694088, 1880304, 3290112, 14839968, 22472640, 17805312, 42407136, 117876096, 327661128, 178588800, 561863168, 1604383200
Offset: 2

Views

Author

Roger L. Bagula, Jun 09 2005

Keywords

Links

Crossrefs

Cf. A000010, A000073, A065449, A197218, A272040.

Programs

  • Mathematica
    F[1] = 0; F[2] = 1; F[3] = 1; F[n__] := F[n] = F[n - 1] + F[n - 2] + F[n - 3]; Table[EulerPhi[F[n]], {n, 2, 50}]

Formula

a(n) = A000010(A000073(n)). - Amiram Eldar, Mar 02 2020

Extensions

First term 0 removed and offset corrected by Amiram Eldar, Mar 02 2020

A366773 a(n) = A000010(A001045(n)).

Original entry on oeis.org

1, 1, 2, 4, 10, 12, 42, 64, 108, 300, 682, 576, 2730, 5292, 6600, 16384, 43690, 46656, 174762, 240000, 455112, 1320352, 2796202, 2211840, 10125000, 22358700, 28256040, 66382848, 175923744, 178200000, 715827882, 1073741824, 1877540544, 5726448300, 10133592000
Offset: 1

Views

Author

Sean A. Irvine, Oct 21 2023

Keywords

Links

Crossrefs

Cf. A000010, A001045, A065449, A197218, A272040.

Formula

a(n) = phi(A001045(n)).
Showing 1-6 of 6 results.

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