A372599 -id:A372599 - cp's OEIS frontend

A372546 Number of distinct prime factors of n^n+n.

1, 2, 3, 3, 3, 5, 5, 4, 3, 7, 4, 4, 4, 8, 6, 5, 5, 6, 10, 6, 6, 10, 6, 5, 6, 8, 8, 11, 6, 7, 11, 7, 7, 13, 7, 9, 8, 7, 5, 10, 7, 7, 12, 7, 9, 18, 6, 7, 10, 10, 11, 11, 10, 9, 14, 12, 12, 11, 7, 9, 13, 6, 7, 16, 5, 14, 10, 7, 7, 15, 11, 7, 13, 7, 8, 16, 9, 13

Offset: 1

Tyler Busby, May 06 2024

nonn

Amiram Eldar, Table of n, a(n) for n = 1..116

Cf. A001221, A066068, A372599, A372228, A344870, A344869, A377671.

a[n_] := PrimeNu[n^n + n]; Array[a, 40] (* Amiram Eldar, Oct 29 2024 *)

PARI
```
a(n) = omega(n^n+n);
```

from sympy.ntheory.factor_ import primenu
def A372546(n): return primenu(n*(n**(n-1)+1)) # Chai Wah Wu, May 07 2024

a(n) = A001221(A066068(n)).

A377675 Number of prime factors of n^n-n (counted with multiplicity).

Original entry on oeis.org

1, 4, 5, 7, 5, 9, 7, 12, 8, 9, 7, 13, 6, 11, 17, 16, 6, 17, 7, 15, 10, 10, 10, 19, 11, 18, 15, 14, 7, 22, 13, 21, 11, 14, 22, 24, 7, 15, 15, 26, 9, 20, 7, 17, 17, 12, 11, 30, 9, 24, 15, 20, 10, 29, 16, 27, 12, 13, 9, 29, 8, 18, 29, 27, 15, 24, 8, 23, 13, 25

Offset: 2

Sean A. Irvine, Nov 03 2024

nonn

Amiram Eldar, Table of n, a(n) for n = 2..115

Cf. A001222, A061190, A309941, A372229, A372599, A377671, A377676, A377677, A377678.

a[n_] := PrimeOmega[n^n - n]; Array[a, 45, 2] (* Amiram Eldar, Nov 04 2024 *)

PARI
```
a(n) = bigomega(n^n-n);
```

a(n) = A001222(A061190(n)).

A377676 a(n) is the number of divisors of n^n - n.

Original entry on oeis.org

2, 8, 18, 40, 24, 120, 48, 336, 80, 192, 72, 1920, 48, 288, 23040, 1728, 36, 10240, 72, 7680, 432, 240, 384, 32256, 640, 49152, 2016, 3840, 96, 193536, 1152, 22528, 1152, 4608, 1327104, 1638400, 96, 7680, 9216, 4128768, 384, 294912, 72, 23040, 30720, 576

Offset: 2

Sean A. Irvine, Nov 03 2024

nonn

Amiram Eldar, Table of n, a(n) for n = 2..115

Cf. A000005, A061190, A334167, A372229, A372599, A377672, A377675, A377677, A377678.

a[n_] := DivisorSigma[0, n^n - n]; Array[a, 45, 2] (* Amiram Eldar, Nov 04 2024 *)

PARI
```
a(n) = numdiv(n^n-n);
```

a(n) = A000005(A061190(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

Sean A. Irvine, Nov 03 2024

nonn

Amiram Eldar, Table of n, a(n) for n = 2..115

Cf. A000010, A061190, A366821, A372229, A372599, A377674, A377675, A377676, A377677.

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

PARI
```
a(n) = eulerphi(n^n-n);
```

a(n) = A000010(A061190(n)).

cp's OEIS Frontend

A372546 Number of distinct prime factors of n^n+n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A377675 Number of prime factors of n^n-n (counted with multiplicity).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A377676 a(n) is the number of divisors of n^n - n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula