A085723 -id:A085723 - cp's OEIS frontend

A309941 Number of prime factors of n^n - 1, counted with multiplicity.

1, 2, 3, 4, 4, 4, 7, 8, 6, 4, 8, 6, 5, 7, 7, 7, 10, 4, 11, 10, 8, 6, 13, 13, 11, 9, 13, 10, 15, 4, 13, 12, 13, 10, 18, 11, 8, 10, 16, 9, 16, 6, 15, 18, 9, 5, 19, 20, 14, 15, 17, 8, 16, 12, 18, 10, 10, 5, 26, 8, 10, 14, 20, 19, 17, 9, 17, 12, 19, 7, 29, 15, 8, 11, 20, 13, 21, 8

Offset: 2

Hugo Pfoertner, Aug 24 2019

			a(3) = 2: 3^3 - 1 = 26 = 2 * 13.
a(5) = 4: 5^5 - 1 = 3124 = 2^2 * 11 * 71.

Amiram Eldar, Table of n, a(n) for n = 2..138 (terms 2..126 from Chai Wah Wu)
factordb, Factors of n^n-1.

Cf. A006486, A048861, A085723, A116895, A125135, A334167, A344870.

a[n_] := PrimeOmega[n^n - 1]; Array[a, 45, 2] (* Amiram Eldar, Jul 04 2024 *)

for(k=2, 50, print1(bigomega(k^k-1),", "))

A366899 Number of prime factors of n*2^n - 1, counted with multiplicity.

Original entry on oeis.org

0, 1, 1, 3, 2, 1, 2, 2, 2, 2, 3, 2, 4, 5, 4, 6, 3, 2, 3, 2, 4, 5, 3, 3, 2, 3, 3, 4, 5, 1, 3, 2, 3, 5, 3, 5, 2, 3, 2, 5, 4, 3, 5, 3, 4, 5, 7, 4, 4, 3, 3, 4, 5, 3, 4, 3, 4, 3, 5, 3, 3, 4, 3, 9, 6, 4, 4, 6, 4, 3, 3, 2, 5, 4, 1, 9, 3, 4, 5, 2, 1, 4, 5, 6, 2, 3, 4

Offset: 1

Tyler Busby, Oct 26 2023

nonn

The numbers n*2^n-1 are called Woodall (or Riesel) numbers.

Amiram Eldar, Table of n, a(n) for n = 1..865

Cf. A001222, A003261, A085723, A366898 (divisors), A367006 (without multiplicity).

Table[PrimeOmega[n*2^n - 1], {n, 1, 100}] (* Amiram Eldar, Dec 09 2023 *)

a(n) = bigomega(n*2^n - 1); \\ Michel Marcus, Dec 09 2023

a(n) = bigomega(n*2^n - 1) = A001222(A003261(n)).

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

Sean A. Irvine, Nov 03 2024

nonn

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

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

seq(numtheory:-bigomega(n^n+n),n=1..76); # Robert Israel, Nov 03 2024

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

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

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

A344869 Number of distinct prime factors of n^n+1.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 3, 3, 3, 4, 3, 6, 4, 5, 5, 6, 2, 3, 7, 5, 3, 6, 4, 8, 6, 7, 5, 11, 6, 7, 10, 7, 4, 11, 6, 13, 5, 7, 7, 8, 9, 6, 10, 8, 8, 14, 8, 10, 6, 7, 10, 11, 5, 8, 14, 11, 7, 13, 13, 9, 12, 8, 7, 18, 4, 12, 8, 7, 7, 16, 9, 8, 12, 4, 8, 24, 7, 9, 14, 7, 5, 12, 6, 12, 8, 13, 10, 12, 10, 6, 23, 15, 6, 9, 11, 16, 3, 8, 17, 23, 7

Offset: 0

Seiichi Manyama, May 31 2021

nonn

Amiram Eldar, Table of n, a(n) for n = 0..148
Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind.

Cf. A001221, A014566, A085723, A128428, A344859, A344870.

Magma
```
[#PrimeDivisors(n^n+1): n in [0..100]];
```

a[0] = 1; a[n_] := PrimeNu[n^n + 1]; Array[a, 45, 0] (* Amiram Eldar, May 31 2021 *)

PARI
```
a(n) = omega(n^n+1);
```

a(n) = A001221(A014566(n)).

a(67)-a(79) from Jon E. Schoenfield, May 31 2021

a(80)-a(100) from Seiichi Manyama, May 31 2021

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A309941 Number of prime factors of n^n - 1, counted with multiplicity.

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A366899 Number of prime factors of n*2^n - 1, counted with multiplicity.

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

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A344869 Number of distinct prime factors of n^n+1.

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