A103890 -id:A103890 - 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.

A103892 Greatest prime factor of prime(n)! / prime(n)# + 1.

Original entry on oeis.org

2, 2, 5, 5, 1571, 2693, 15427, 27749, 4154449757, 151585363459003, 73899633146196133, 24770877398207, 1429176066859677377, 7748318379505746557, 21662673895172922098651, 447620901583917369406703727865417431168683, 26823894708473887265117477378744683922119

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..30
Reinhard Zumkeller, prime(n)! / prime(n)# + 1.

Cf. A006530, A103857, A103890, A103891.

a(n) = A006530(A103890(n)).

A103895 Sum of divisors of prime(n)! / prime(n)# + 1.

Original entry on oeis.org

3, 3, 6, 31, 18864, 258624, 733755680, 13213440000, 115884221549652, 1372805558801047105280, 40999368670243322750932, 1855053929165456908669711085568, 113895178720398409713058206857404800, 4701294182073054820056713442085236768

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..30
Reinhard Zumkeller, prime(n)! / prime(n)# + 1.

Cf. A000203, A103860, A103890, A103894.

a(n) = A000203(A103890(n)).

A103891 Smallest prime factor of prime(n)! / prime(n)# + 1.

Original entry on oeis.org

2, 2, 5, 5, 11, 7, 19, 31, 27893, 223, 554797, 10333, 29, 61, 28652131, 293049347, 7731517, 1483, 73, 337809273983, 67, 440939, 1321, 94099, 89, 107, 281, 1908113757161297657, 479, 61, 167, 3121, 177907, 5039, 11519, 281, 612153149, 587, 2753, 21491, 2897, 97, 307

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

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

Cf. A020639, A103856, A103890, A103892.

a(n) = A020639(A103890(n)).

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

More terms from Jinyuan Wang, Apr 16 2020

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

A103896 Euler's totient of prime(n)! / prime(n)# + 1.

Original entry on oeis.org

1, 1, 4, 20, 15700, 161520, 659739168, 11887243200, 115875912594352, 1360481062410358294032, 40999220870977029249072, 1854483563489396099991763032000, 106016408292727234808287504322403328, 4534810991759912394035394805790730240

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..30
Reinhard Zumkeller, prime(n)! / prime(n)# + 1.

Cf. A000010, A103861, A103890.

a(n) = A000010(A103890(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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A103892 Greatest prime factor of prime(n)! / prime(n)# + 1.

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A103895 Sum of divisors of prime(n)! / prime(n)# + 1.

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A103891 Smallest prime factor of prime(n)! / prime(n)# + 1.

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

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A103896 Euler's totient 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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