A372229 -id:A372229 - cp's OEIS frontend

A372228 a(n) is the largest prime factor of n^n + n.

2, 3, 5, 13, 313, 101, 181, 5419, 21523361, 52579, 212601841, 57154490053, 815702161, 100621, 4454215139669, 4562284561, 52548582913, 1895634885375961, 211573, 2272727294381, 415710882920521, 9299179, 1853387306082786629, 22496867303759173834520497

Offset: 1

Tyler Busby, Apr 23 2024

nonn

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

Cf. A066068, A006530, A006486, A007571, A372229.

Table[f = FactorInteger[n^n + n]; f[[Length[f]]][[1]], {n, 1, 25}] (* Vaclav Kotesovec, Apr 26 2024 *)

from sympy import primefactors
def A372228(n): return max(max(primefactors(n),default=1),max(primefactors(n**(n-1)+1))) # Chai Wah Wu, Apr 27 2024

a(n) = A006530(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

Tyler Busby, May 06 2024

nonn

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

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

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);
```

from sympy.ntheory.factor_ import primenu
def A372599(n): return primenu(n*(n**(n-1)-1)) # Chai Wah Wu, May 07 2024

a(n) = A001221(A061190(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

A372228 a(n) is the largest prime factor of n^n + n.

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

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

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

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

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