A103858 -id:A103858 - 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.

A103859 Number of divisors of prime(n)! - prime(n)# + 1.

Original entry on oeis.org

1, 1, 4, 2, 4, 4, 4, 4, 16, 4, 8, 16, 16, 32, 32, 8, 32, 8, 16, 64, 32, 16, 32, 64, 512, 2, 16

Offset: 1

Reinhard Zumkeller, Feb 20 2005

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

Cf. A000005, A103855, A103858, A103860, A103894.

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

a(n) = A000005(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)).

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

Original entry on oeis.org

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

Reinhard Zumkeller, Feb 20 2005

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

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.

Cf. A001221, A103858, A103890.

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 *)

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

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

cp's OEIS Frontend

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

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A103859 Number of divisors of prime(n)! - prime(n)# + 1.

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

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

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