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 1-5 of 5 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

Links

Crossrefs

Cf. A001222, A066068, A085723, A372228, A372546, A377672, A377673, A377674.

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)).

A372599 Number of distinct prime factors of n^n-n.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 4, 6, 5, 6, 5, 9, 5, 6, 12, 8, 4, 10, 5, 11, 7, 6, 7, 12, 8, 13, 8, 10, 6, 14, 8, 12, 9, 10, 18, 18, 6, 11, 11, 19, 8, 16, 5, 12, 13, 7, 7, 20, 5, 18, 12, 14, 7, 21, 12, 19, 10, 10, 7, 24, 7, 10, 20, 15, 13, 19, 6, 19, 11, 19, 9, 25, 6, 13
Offset: 2

Views

Author

Tyler Busby, May 06 2024

Keywords

Links

Crossrefs

Cf. A001221, A061190, A372546, A372229, A344870, A344869.

Programs

  • Mathematica
    a[n_] := a[n] = PrimeNu[n^n - n];
Table[a[n], {n, 2, 75}] (* Robert P. P. McKone, May 07 2024 *)
  • PARI
    a(n) = omega(n^n-n);
  • Python
    from sympy.ntheory.factor_ import primenu
def A372599(n): return primenu(n*(n**(n-1)-1)) # Chai Wah Wu, May 07 2024

Formula

a(n) = A001221(A061190(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

Links

Crossrefs

Cf. A000005, A066068, A344859, A372228, A372546, A377671, A377673, A377674.

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

Links

Crossrefs

Cf. A000203, A066068, A366820, A372228, A372546, A377671, A377672, A377674.

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)).

A377674 a(n) = phi(n^n + n) where phi is the Euler totient function.

Original entry on oeis.org

1, 2, 8, 96, 1248, 12000, 259200, 5461344, 129140160, 2725643520, 127561104000, 2743415522496, 139778722137600, 2504616361228800, 111747349423990784, 8644660582219776000, 387774574486565683200, 12306643656809728412160, 816897235219321957908480
Offset: 1

Views

Author

Sean A. Irvine, Nov 03 2024

Keywords

Links

Crossrefs

Cf. A000010, A066068, A366822, A372228, A372546, A377671, A377672, A377673.

Programs

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

Formula

a(n) = A000010(A066068(n)).
Showing 1-5 of 5 results.

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