A103859 -id:A103859 - cp's OEIS frontend

A103855 a(n) = prime(n)! - prime(n)# + 1.

1, 1, 91, 4831, 39914491, 6226990771, 355687427585491, 121645100399132311, 25852016738884753547131, 8841761993739701954537146306771, 8222838654177922817725362319509871, 13763753091226345046315979581573481661865191, 33452526613163807108170062053440751360901736472791

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

G. C. Greubel, Table of n, a(n) for n = 1..86
Reinhard Zumkeller, p(n)! - p(n)# + 1.

Cf. A103856, A103857, A103858, A103859, A103860, A103861, A103890.

Cf. A002110, A039716, A092435.

primorial[n_] := Product[Prime[i], {i, n}]; A103855[n_] := Prime[n]! - primorial[n] + 1; Array[A103855, 20] (* G. C. Greubel, May 09 2017 *)
With[{nn=15},#[[1]]-#[[2]]+1&/@Thread[{Prime[Range[nn]]!,FoldList[Times,Prime[Range[nn]]]}]] (* Harvey P. Dale, Aug 11 2025 *)

a(n) = A039716(n) - A002110(n) + 1 = A002110(n) * (A092435(n) - 1) + 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

A103860 Sum of divisors of prime(n)! - prime(n)# + 1.

Original entry on oeis.org

1, 1, 112, 4832, 39929032, 6227388000, 355687500698712, 121674349040732800, 26204303786955547121568, 8844022735747817449795273936944, 8243360285859647409507002537385024, 13989390090648918627329493090109449081402880, 33452526614068666040537953433982904696696861440000

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..26
Reinhard Zumkeller, p(n)! - p(n)# + 1.

Cf. A000203, A103855, A103858, A103859, A103895.

Module[{nn=15,pr,pm},pr=Prime[Range[nn]]!;pm=FoldList[Times,Prime[Range[nn]]];DivisorSigma[1,#[[1]]-#[[2]]+1&/@Thread[{pr,pm}]]] (* Harvey P. Dale, Dec 18 2022 *)

a(n) = sigma(prime(n)! - factorback(primes(n)) + 1); \\ Jinyuan Wang, Dec 28 2024

a(n) = A000203(A103855(n)).

A103894 Number of divisors of prime(n)! / prime(n)# + 1.

Original entry on oeis.org

2, 2, 2, 3, 4, 8, 8, 16, 4, 8, 4, 16, 16, 32, 8, 4, 8, 16, 64, 32, 32, 32, 32, 64, 32, 16, 32, 8, 128, 32

Offset: 1

Reinhard Zumkeller, Feb 20 2005

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

Cf. A000005, A103859, A103890, A103895.

a(n) = A000005(A103890(n)).

a(28)-a(30) from Amiram Eldar, Feb 13 2020

cp's OEIS Frontend

A103855 a(n) = prime(n)! - prime(n)# + 1.

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

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A103860 Sum of divisors of prime(n)! - prime(n)# + 1.

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A103894 Number of divisors of prime(n)! / prime(n)# + 1.

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