A103858 Number of distinct prime factors of prime(n)! - prime(n)# + 1.

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

Offset: 1

Author

Reinhard Zumkeller, Feb 20 2005

Keywords

• nonn
• more

Comments

a(27) >= 4. - Amiram Eldar, Jan 21 2024

Links

• Factordb.com, Status of 107! - 107# + 1.
• Reinhard Zumkeller, prime(n)! - prime(n)# + 1.

Crossrefs

Cf. A001221, A103855, A103859, A103893.

Programs

Mathematica

primorial[n_] := Product[Prime[i], {i, n}]; A103855[n_] := Prime[n]! - primorial[n] + 1;  PrimeNu[Array[A103855, 20]] (* G. C. Greubel, May 09 2017 *)

PARI

a(n) = omega(prime(n)! - prod(k=1, n, prime(k)) + 1); \\ Michel Marcus, Nov 06 2022

Formula

a(n) = A001221(A103855(n)).

Extensions

a(27) from Jinyuan Wang, Jun 19 2025