A103893 -id:A103893 - cp's OEIS frontend

A103890 a(n) = prime(n)! / prime(n)# + 1.

2, 2, 5, 25, 17281, 207361, 696729601, 12541132801, 115880067072001, 1366643159020339200001, 40999294770610176000001, 1854768736099424576471040000001, 109950690675973888893203251200000001, 4617929008390903333514536550400000001

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

Reinhard Zumkeller, p(n)! / p(n)# + 1.

Cf. A103855, A103891, A103892, A103893, A103894, A103895, A103896.

#[[1]]/#[[2]]&/@With[{nn=15},Thread[{Prime[Range[nn]]!,FoldList[ Times,Prime[ Range[nn]]]}]]+1 (* Harvey P. Dale, May 21 2019 *)

a(n) = prime(n)!/vecprod(primes(n)) + 1; \\ Michel Marcus, Nov 12 2023

a(n) = A039716(n)/A002110(n) + 1 = A092435(n) + 1.

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

Original entry on oeis.org

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

Reinhard Zumkeller, Feb 20 2005

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

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

Cf. A001221, A103855, A103859, A103893.

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

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

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

a(27) from Jinyuan Wang, Jun 19 2025

cp's OEIS Frontend

A103890 a(n) = prime(n)! / prime(n)# + 1.

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