login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113905 omega(n!) raised to the power of bigomega(n!). 0
1, 1, 1, 4, 16, 243, 2187, 65536, 4194304, 67108864, 1073741824, 152587890625, 19073486328125, 3656158440062976, 131621703842267136, 4738381338321616896, 6140942214464815497216, 3219905755813179726837607 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Sum of reciprocals converge to 3.317087986755007857557474300.. I found getting the 3 starting 1's interesting. 6 sequences begin with 1,1,1,4,16 and none begin with omegafactpowbigomegafact(n) = 1,1,1,4,16,243.

LINKS

Table of n, a(n) for n=0..17.

FORMULA

omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.

a(n) = A000720(n)^A022559(n). - Reinhard Zumkeller, Feb 01 2006

MATHEMATICA

Join[{1, 1}, PrimeNu[#]^PrimeOmega[#]&/@(Range[2, 20]!)] (* Harvey P. Dale, Aug 07 2022 *)

PROG

(PARI) omegafactpowbigomegafact(n) = { local(x, a, b, s); s=0; for(x=0, n, a=omega(x!); b=bigomega(x!); s+=1./a^b; print1(a^b", "); ); print(); print(s) }

CROSSREFS

Sequence in context: A271267 A333438 A232840 * A200045 A099202 A139288

Adjacent sequences:  A113902 A113903 A113904 * A113906 A113907 A113908

KEYWORD

easy,nonn,changed

AUTHOR

Cino Hilliard, Jan 29 2006

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 18 10:34 EDT 2022. Contains 356212 sequences. (Running on oeis4.)