A177926 -id:A177926 - cp's OEIS frontend

A178056 Integers equal to ((sqrt(A177926(k)/400)/4)/600)/36 for some k.

12108096, 3705077376, 650463384130560, 176440014242889965568000, 153502812391314270044160000, 215273915966378019368055236198400000, 472173196324014892561117632868122624000000, 813082244069953644990244563798907158528000000

Offset: 1

Giovanni Teofilatto, May 19 2010

Cf. A177771, A177926.

A177771 := proc(n) factorial(ithprime(n)-1) ; end proc:
A178056 := proc(n) A177771(n+6)/1728000 ; end proc: seq(A178056(n),n=1..10) ; # R. J. Mathar, May 24 2010

a(n) = A177771(n+6)/1728000. - R. J. Mathar, May 24 2010

A177771 a(n) = (prime(n) - 1)!.

Original entry on oeis.org

1, 2, 24, 720, 3628800, 479001600, 20922789888000, 6402373705728000, 1124000727777607680000, 304888344611713860501504000000, 265252859812191058636308480000000

Offset: 1

Giovanni Teofilatto, May 13 2010

nonn

By Wilson's theorem, a(n) = -1 (mod p) where p is the n-th prime. - Charles R Greathouse IV, Sep 04 2013

Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 21.

Vincenzo Librandi, Table of n, a(n) for n = 1..80

Cf. A006093, A039716.

[Factorial(p-1): p in PrimesUpTo(20)]; // Vincenzo Librandi, May 31 2013

(Prime[Range[12]]-1)! (* Harvey P. Dale, Jul 12 2011 *)

apply(p->(p-1)!,primes(10)) \\ Charles R Greathouse IV, Sep 04 2013

a(n) = A010050(A005097(n-1)). a(n)^2 = A177926(n). - R. J. Mathar, May 24 2010

A177963 a(n) = ((prime(n) - 3)!)^2.

Original entry on oeis.org

1, 4, 576, 1625702400, 13168189440000, 7600054456551997440000, 437763136697395052544000000, 5919012181389927685417441689600000000, 162644002617632464507038883409628607021056000000000000

Offset: 2

Giovanni Teofilatto, May 16 2010

Except for the first three terms, sqrt(a(n)/400) is an integer. For all terms a(n), sqrt(a(n+1)/a(n)) is an integer.

Nathaniel Johnston, Table of n, a(n) for n = 2..50

Cf. A177926.

A177963 := proc(n) return factorial(ithprime(n)-3)^2: end: seq(A177963(n),n=2..10); # Nathaniel Johnston, May 28 2011

((Prime[Range[2,10]]-3)!)^2 (* Harvey P. Dale, Jun 28 2023 *)

Offset corrected by Nathaniel Johnston, May 28 2011

A180369 A177771(n+3)/6! .

Original entry on oeis.org

1, 5040, 665280, 29059430400, 8892185702400, 1561112121913344000, 423456034182935917363200000, 368406749739154248105984000000, 516657398319307246483332566876160000000

Offset: 1

Giovanni Teofilatto, Aug 31 2010

nonn

Cf. A178056.

a(n) = sqrt( A177926(n+3) )/720.

Parentheses and indices corrected - R. J. Mathar, Sep 03 2010

cp's OEIS Frontend

A178056 Integers equal to ((sqrt(A177926(k)/400)/4)/600)/36 for some k.

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A177771 a(n) = (prime(n) - 1)!.

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A177963 a(n) = ((prime(n) - 3)!)^2.

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A180369 A177771(n+3)/6! .

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