login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054991 Number of prime divisors of n! - 1. 7
0, 0, 1, 1, 2, 1, 1, 2, 3, 2, 4, 1, 2, 1, 5, 2, 3, 3, 3, 2, 4, 3, 2, 2, 3, 2, 2, 4, 5, 1, 3, 1, 1, 2, 3, 2, 5, 1, 4, 2, 4, 4, 7, 4, 5, 5, 2, 4, 3, 2, 5, 5, 4, 6, 6, 5, 6, 5, 2, 3, 4, 4, 5, 4, 6, 4, 7, 2, 6, 5, 5, 3, 4, 5, 7, 3, 5, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The series is related to the product of primes and the "proof" of the existence of infinite many prime twins.

LINKS

Table of n, a(n) for n=1..78.

R. G. Wilson v, Explicit factorizations

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

EXAMPLE

a(2)=0 because 2! - 1 = 1 (and this is not a prime number) a(5)=2 because 5! -1 = 119 = 7 * 17

MATHEMATICA

a[q_] := Module[{x, n}, x=FactorInteger[q!-1]; n=Length[x]; Sum[Table[x[[i]][[2]], {i, n}][[j]], {j, n}]]

A054991[n_Integer] := PrimeOmega[n! - 1]; A054991[1] = 0; Table[A054991[n], {n, 2, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

CROSSREFS

Cf. A054988, A054989, A054990, A054992.

Sequence in context: A114919 A087917 A087741 * A302918 A316149 A047071

Adjacent sequences:  A054988 A054989 A054990 * A054992 A054993 A054994

KEYWORD

nonn

AUTHOR

Arne Ring (arne.ring(AT)epost.de), May 30 2000

EXTENSIONS

More terms from Robert G. Wilson v, Mar 24 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 06:14 EST 2018. Contains 317162 sequences. (Running on oeis4.)