A039716 -id:A039716 - cp's OEIS frontend

A178614 a(n) = prime(n)!/(n+1)!.

1, 1, 5, 42, 55440, 1235520, 8821612800, 335221286400, 7124122778572800, 221504779785446277120000, 17166620433372086476800000, 2210327142511928825790332928000000

Offset: 1

Juri-Stepan Gerasimov, Jun 05 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 1..75

[Factorial(NthPrime(n))/Factorial(n+1): n in [1..15]]; // G. C. Greubel, Jan 29 2019

Table[(Prime[n])!/(n+1)!, {n, 1, 15}] (* G. C. Greubel, Jan 29 2019 *)

vector(15, n, (prime(n))!/(n+1)!) \\ G. C. Greubel, Jan 29 2019

[factorial(nth_prime(n))/factorial(n+1) for n in (1..15)] # G. C. Greubel, Jan 29 2019

a(n) = A039716(n)/A000142(n+2) = A177946(n)/(n+1).

a(7) and a(9) corrected by R. J. Mathar, Jun 07 2010

A181576 Primes whose factorials end with a prime number of trailing 0's.

Original entry on oeis.org

11, 13, 17, 19, 31, 59, 83, 127, 151, 173, 179, 197, 199, 223, 293, 367, 397, 421, 439, 449, 461, 463, 557, 569, 607, 617, 619, 631, 659, 733, 773, 797, 853, 919, 941, 967, 1013, 1039, 1061, 1063, 1087, 1097, 1123, 1181, 1259, 1399, 1423, 1447, 1543, 1567

Offset: 1

Lekraj Beedassy, Nov 02 2010

For the corresponding prime number of trailing end 0's, see A181577.

			The factorial 2! = 2 ends with 0 zeros, so the prime 2 is not in the sequence because 0 is not a prime.
The factorial 5! = 120 ends with 1 zero, so the prime 5 is not in the sequence because 1 is not a prime.
The factorial 11! = 39916800 ends with 2 zeros, so the prime 11 is in the sequence because 2 is a prime.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A027868, A039716, A181577.

Select[ Prime@ Range@ 250, PrimeQ@ IntegerExponent[ #! ] &] (* Robert G. Wilson v, Nov 06 2010 *)

is(p) = isprime(p) && isprime((p - sumdigits(p, 5))/4); \\ Amiram Eldar, May 03 2024

A027868(a(n)) = A181577(n). - Amiram Eldar, May 03 2024

More terms from Robert G. Wilson v, Nov 06 2010

A260754 a(n) = prime(n+1)! / prime(n).

Original entry on oeis.org

3, 40, 1008, 5702400, 566092800, 27360571392000, 7155594141696000, 1360632459941314560000, 384424434510421824110592000000, 283546160488893890266398720000000

Offset: 1

Altug Alkan, Aug 20 2015

			a(2) = 5! / 3 = 40.

Cf. A000040, A039716, A072472.

[Factorial(NthPrime(n+1))/NthPrime(n) : n in [1..10]]; // Wesley Ivan Hurt, Aug 20 2015

A260754:=n->ithprime(n+1)!/ithprime(n): seq(A260754(n), n=1..20); # Wesley Ivan Hurt, Aug 20 2015

Table[Prime[i+1] !/Prime[i], {i,20}] (* G. C. Greubel, Aug 20 2015 *)

vector(15, n, prime(n+1)!/prime(n)) \\ Michel Marcus, Aug 20 2015

a(n) = prime(n+1)! / prime(n) = A039716(n+1) / A000040(n).

10^(n-1)|a(n+3) for n>=0. - G. C. Greubel, Aug 20 2015

A262206 Product of prime(n) consecutive numbers starting from n.

Original entry on oeis.org

2, 24, 2520, 604800, 54486432000, 53353114214400, 35905578804006912000, 80018147048929689600000, 203939450748460387344384000000, 1441310123089178548721360295690240000000, 9218619547278385997621820451234775040000000

Offset: 1

Altug Alkan, Sep 15 2015

a(n) is always divisible by A039716(n).

			For n=1, a(1) = 1*2 = 2.
For n=2, a(2) = 2*3*4 = 24.
For n=3, a(3) = 3*4*5*6*7 = 2520.
For n=4, a(4) = 4*5*6*7*8*9*10 = 604800.

Cf. A075069: product of prime(n) consecutive numbers starting from prime(n).

Cf. A014688, A039716, A075068, A262204.

[Factorial(NthPrime(n)+n-1)/Factorial(n-1): n in [1..15]]; // Vincenzo Librandi, Sep 16 2015

A262206:=n->(ithprime(n)+n-1)! / (n-1)!: seq(A262206(n), n=1..15); # Wesley Ivan Hurt, Sep 15 2015

Table[(Prime[n] + n - 1)!/(n - 1)!, {n, 15}] (* Michael De Vlieger, Sep 15 2015 *)

a(n) = (prime(n)+n-1)! / (n-1)!;
vector(15,n,a(n))

a(n)=factorback([n..n+prime(n)-1]) \\ Charles R Greathouse IV, Sep 21 2015

a(n) = (prime(n) + n - 1)! / (n-1)!.

A061024 a(n) = (prime(n)!)^2.

Original entry on oeis.org

4, 36, 14400, 25401600, 1593350922240000, 38775788043632640000, 126513546505547170185216000000, 14797530453474819213543604224000000, 668326769467589022464821184293345689600000000, 78176755153939869305210274200729021751146846355456000000000000

Offset: 1

Jason Earls, May 25 2001

nonn

Harry J. Smith, Table of n, a(n) for n = 1..54 [Offset adapted by _Georg Fischer_, Jul 11 2022]

Cf. A000040, A039716.

(Prime[Range[10]]!)^2 (* Harvey P. Dale, Mar 22 2020 *)

{ n=0; forprime (p=2, prime(54), write("b061024.txt", n++, " ", p!*p!) ) } \\ Harry J. Smith, Jul 16 2009

More terms from Dean Hickerson, Jun 08 2001

Offset corrected by Georg Fischer, Apr 04 2022

A061025 a(n) = prime(n-1)! * prime(n)!.

Original entry on oeis.org

12, 720, 604800, 201180672000, 248562743869440000, 2214873013052296396800000, 43267632904897132203343872000000, 3144771171972468579262286769684480000000, 228577379063395778964892338453378050021130240000000000, 72704382293164078453845555006677990228566567110574080000000000000

Offset: 2

Jason Earls, May 25 2001

nonn

Harry J. Smith, Table of n, a(n) for n = 2..54

Cf. A039716.

a[n_]:=Prime[n-1]!*Prime[n]!; Array[a,8,2] (* Stefano Spezia, Aug 02 2024 *)

{ n=1; f=2; forprime (p=3, prime(54), g=p!; write("b061025.txt", n++, " ", f*g); f=g ) } \\ Harry J. Smith, Jul 16 2009

More terms from Harry J. Smith, Jul 16 2009

Definition offset corrected by Stefano Spezia, Aug 02 2024

A111179 a(n) = Sum_{k=1..n} prime(k)!, where prime(k) is k-th prime.

Original entry on oeis.org

2, 8, 128, 5168, 39921968, 6266942768, 355693695038768, 122000794103870768, 25852138739679080510768, 8841762019591840694222696510768, 8231680416197514658419785576510768, 13763753099458025462513494240000687976510768

Offset: 1

Leroy Quet, Oct 22 2005

			2, 3, 5 and 7 are the first 4 primes. So a(4) = 2! + 3! + 5! + 7! = 2 +6 +120 +5040 = 5168.

Cf. A039716.

Table[ Sum[ Prime[i]!, {i, n}], {n, 12}] (* Robert G. Wilson v, Oct 28 2005 *)

a(n)=sum(k=1,n,prime(k)!) \\ Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 28 2005

More terms from Lambert Klasen (lambert.klasen(AT)gmx.net) and Robert G. Wilson v, Oct 28 2005

A111180 Product_{k=1..n} prime(k)!.

Original entry on oeis.org

1, 2, 12, 1440, 7257600, 289700167680000, 1803968969906847744000000, 641649083271157094762019815424000000000, 78053467161754909919949074014980107579424768000000000000

Offset: 0

Leroy Quet, Oct 22 2005

			2, 3, 5 and 7 are the first 4 primes. So a(4) = 2! * 3! * 5! * 7! = 2 *6 *120 *5040 = 7257600.

Cf. A039716.

Table[ Product[ Prime[i]!, {i, n}], {n, 0, 8}] (* Robert G. Wilson v *)
FoldList[Times,1,Prime[Range[10]]!] (* Harvey P. Dale, Apr 08 2012 *)

More terms from Robert G. Wilson v, Oct 29 2005

A157132 Factorial of primes divided by prime numbers' respective places in the sequence of primes.

Original entry on oeis.org

2, 3, 40, 1260, 7983360, 1037836800, 50812489728000, 15205637551104000, 2872446304320552960000, 884176199373970195454361600000, 747530786743447528884142080000000

Offset: 1

Jeremy Cahill (jcahill(AT)inbox.com), Feb 23 2009

			E.g. leading term = 2!/1 = 2, second term = 3!/2 = 3, third term = 5!/3 = 40, etc.

Terms of A039716 divided by sequence of natural numbers A000027

Cf. A177946. [From Reinhard Zumkeller, May 15 2010]

Table[Prime[n]!/n,{n,20}] (* Harvey P. Dale, May 24 2017 *)

a(n) = prime(n)!/n; \\ Michel Marcus, Aug 19 2013

a(n) = prime(n)!/n.

A181573 Impossible numbers of trailing zeros in the decimal representation of a factorial of any prime.

Original entry on oeis.org

5, 11, 17, 21, 23, 27, 28, 29, 30, 34, 36, 42, 45, 48, 49, 50, 52, 54, 59, 60, 61, 67, 70, 72, 73, 74, 78, 79, 80, 83, 85, 88, 91, 92, 96, 98, 101, 104, 105, 110, 111, 115, 116, 118, 122, 123, 126, 127, 129, 130, 131, 132, 135, 136, 141, 143, 147, 152, 153, 154, 155

Offset: 1

Lekraj Beedassy, Oct 31 2010

No entry of A039716 ends with 5, 11, 17, 21,... consecutive zeros.

Cf. A000966.

f[n_] := IntegerExponent[Prime@n!, 10]; Complement[ Range[0, 157], Array[f, 115]] (* Robert G. Wilson v, Nov 05 2010 *)
zOF[n_Integer?Positive]:=Module[{maxpow=0},While[5^maxpow<=n,maxpow++];Plus@@Table[ Quotient[n,5^i],{i,maxpow-1}]]; Attributes[zOF]={Listable}; With[{z=Union[zOF[Prime[Range[ 150]]]]},Complement[ Range[Max[z]],z]] (* Harvey P. Dale, Sep 17 2024 *)

Definition rephrased, keyword:base added by R. J. Mathar, Nov 03 2010

More terms from Robert G. Wilson v, Nov 05 2010

cp's OEIS Frontend

A178614 a(n) = prime(n)!/(n+1)!.

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A181576 Primes whose factorials end with a prime number of trailing 0's.

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A260754 a(n) = prime(n+1)! / prime(n).

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A262206 Product of prime(n) consecutive numbers starting from n.

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A061024 a(n) = (prime(n)!)^2.

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A061025 a(n) = prime(n-1)! * prime(n)!.

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A111179 a(n) = Sum_{k=1..n} prime(k)!, where prime(k) is k-th prime.

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