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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A088533 Numbers n such that Bigomega(n!)/Omega(n!) is an integer. 2
2, 3, 4, 7, 15, 22, 24, 40, 49, 58, 71, 74, 92, 124, 179, 183, 232, 237, 413, 542, 547, 731, 752, 758, 983, 1266, 1283, 1289, 1336, 1706, 1712, 1725, 2656, 2909, 3509, 3612, 3653, 3674, 3702, 3709, 4617, 4646, 4697, 5993 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..208

M. Hassani, On the decomposition of n! into primes, arXiv:math/0606316.

FORMULA

Let k = number of prime divisors of n! counted with multiplicity; b = number of distinct prime divisors of n!. Then n is in sequence if k/b is an integer.

EXAMPLE

S(4!) = bigomega(4!) / omega(4!) = 4/2 = 2 so 4 is 3rd term in the sequence.

MATHEMATICA

ointQ[n_]:=Module[{f=n!}, IntegerQ[PrimeOmega[f]/PrimeNu[f]]]; Select[Range[ 2, 6000], ointQ] (* Harvey P. Dale, Dec 07 2013 *)

Omega = Nu = 0; a = {}; Do[If[PrimeQ[n], Nu++]; Omega += PrimeOmega[n];

If[Divisible[Omega, Nu], AppendTo[a, n]], {n, 2, 6000}]; a (* Ivan Neretin, Mar 14 2017 *)

PROG

(PARI) for(x=2, 10000, x1=x!; y=bigomega(x1)/omega(x1); if(y==floor(y), print1((x)", ")))

CROSSREFS

Cf. A000720, A022559.

Sequence in context: A290992 A265742 A098010 * A091155 A254432 A027362

Adjacent sequences:  A088530 A088531 A088532 * A088534 A088535 A088536

KEYWORD

nonn

AUTHOR

Cino Hilliard, Nov 16 2003

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)