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 1-4 of 4 results.

A272040 a(n) = A000010(A000129(n)).

Original entry on oeis.org

1, 1, 4, 4, 28, 24, 156, 128, 784, 1120, 5740, 2880, 33460, 37128, 150080, 147456, 1128256, 931392, 6446016, 4677120, 28514304, 44450560, 224075664, 106168320, 1265644800, 1560708240, 5970392064, 5588803584, 44560482148, 33497856000, 255263424000, 196368924672, 1210784762880
Offset: 1

Views

Author

Altug Alkan, May 06 2016

Keywords

Examples

			a(3) = 4 because a(3) = A000010(A000129(3)) = A000010(5) = 4.

Links

Crossrefs

Cf. A000010, A000129, A000203, A065449, A363829, A363831, A363833, A364818.

Programs

  • Mathematica
    EulerPhi[LinearRecurrence[{2, 1}, {1, 2}, 33]] (* Amiram Eldar, Oct 21 2023 *)
  • PARI
    a000129(n) = ([2,1;1,0]^n)[2,1];
a(n) = eulerphi(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)).
Showing 1-4 of 4 results.

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