A103893 Number of distinct prime factors of prime(n)! / prime(n)# + 1.

1, 1, 1, 1, 2, 3, 3, 4, 2, 3, 2, 4, 4, 5, 3, 2, 3, 4, 6, 5, 5, 5, 5, 6, 5, 4, 5, 3, 7, 5, 5, 8, 5

Offset: 1

Author

Reinhard Zumkeller, Feb 20 2005

Keywords

• nonn
• more

Comments

Also the number of distinct prime factors of the P_n-th compositorial.

a(31) > 4 and its composite part is a 155-digit number.

a(34) >= 4. - Amiram Eldar, Jan 21 2024

Links

• Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
• Factordb.com, Status of 139!/139#+1.
• Hisanori Mishimar, Compositorial + 1 (n = 4 to 150).
• Reinhard Zumkeller, prime(n)!/prime(n)#+1.

Crossrefs

Cf. A001221, A103858, A103890.

Programs

Mathematica

bigomega[n_Integer] := Plus @@ Last /@ FactorInteger[n]; f[n_] := Prime[n]!/Product[Prime[i], {i, n}] + 1; Table[ f[n], {n, 27}] (* Robert G. Wilson v, Mar 11 2005 *)

Formula

a(n) = A001221(A103890(n)).

Extensions

Corrected and extended by Robert G. Wilson v, Mar 12 2005

a(31)-a(33) using factordb.com added by Amiram Eldar, Jan 21 2024