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.

A377671 Number of prime factors of n^n+n (counted with multiplicity).

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 6, 7, 4, 7, 4, 5, 4, 8, 6, 8, 5, 7, 11, 7, 6, 10, 6, 8, 7, 10, 10, 12, 6, 7, 11, 11, 7, 13, 7, 11, 8, 7, 5, 12, 7, 7, 13, 9, 10, 18, 6, 11, 11, 11, 11, 12, 10, 11, 14, 14, 12, 11, 7, 10, 13, 7, 8, 21, 5, 14, 10, 8, 7, 15, 11, 10, 13, 8, 9, 17
Offset: 1

Views

Author

Sean A. Irvine, Nov 03 2024

Keywords

Crossrefs

Programs

  • Maple
    seq(numtheory:-bigomega(n^n+n),n=1..76); # Robert Israel, Nov 03 2024
  • Mathematica
    a[n_] := PrimeOmega[n^n + n]; Array[a, 45] (* Amiram Eldar, Nov 04 2024 *)
  • PARI
    a(n) = bigomega(n^n+n);

Formula

a(n) = A001222(A066068(n)).

A377672 a(n) is the number of divisors of n^n + n.

Original entry on oeis.org

2, 4, 8, 12, 8, 32, 48, 48, 12, 128, 16, 24, 16, 256, 64, 80, 32, 96, 1536, 96, 64, 1024, 64, 96, 96, 512, 512, 3072, 64, 128, 2048, 384, 128, 8192, 128, 1152, 256, 128, 32, 2048, 128, 128, 6144, 288, 768, 262144, 64, 480, 1536, 1536, 2048, 3072, 1024, 1024
Offset: 1

Views

Author

Sean A. Irvine, Nov 03 2024

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := DivisorSigma[0, n^n + n]; Array[a, 45] (* Amiram Eldar, Nov 04 2024 *)
  • PARI
    a(n) = numdiv(n^n+n);

Formula

a(n) = A000005(A066068(n)).

A377673 a(n) is the sum of the divisors of n^n + n.

Original entry on oeis.org

3, 12, 72, 588, 5652, 117504, 1895712, 46503600, 839411118, 25440307200, 474527311344, 22404560101168, 489294047662728, 30902868417576960, 1096805935992340800, 38000593697802058224, 1318965178069293272496, 90596485743469636057920, 3578317312662511683264000
Offset: 1

Views

Author

Sean A. Irvine, Nov 03 2024

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := DivisorSigma[1, n^n + n]; Array[a, 20] (* Amiram Eldar, Nov 04 2024 *)
  • PARI
    a(n) = sigma(n^n+n);

Formula

a(n) = A000203(A066068(n)).

A377678 a(n) = phi(n^n - n) where phi is the Euler totient function.

Original entry on oeis.org

1, 8, 72, 768, 12400, 217728, 7112448, 94371840, 2594586816, 69139840000, 2584376931840, 58779453358080, 4367959006806720, 100089965305451520, 3251736576000000000, 200445251536048619520, 12343971160877345120064, 422076038504126628593664
Offset: 2

Views

Author

Sean A. Irvine, Nov 03 2024

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := EulerPhi[n^n - n]; Array[a, 20, 2] (* Amiram Eldar, Nov 04 2024 *)
  • PARI
    a(n) = eulerphi(n^n-n);

Formula

a(n) = A000010(A061190(n)).
Showing 1-4 of 4 results.