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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A070013 Number of prime factors of n divided by the number of n's distinct prime factors (rounded). 6
1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 3, 4, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

a(n) is the rounded average of the exponents in the prime factorization of n.

LINKS

G. C. Greubel, Table of n, a(n) for n = 2..1000

FORMULA

a(n) = round(bigomega(n)/omega(n)) for n>=2.

EXAMPLE

a(12)=2 because 12=2^2 * 3^1 and round(bigomega(12)/omega(12))=round((2+1)/2)=2.

a(36)=2 because 36=2^2 * 3^2 and round(bigomega(36)/omega(36))=round((2+2)/2)=2.

a(60)=1 because 60=2^2 * 3^1 * 5^1 and round(bigomega(60)/omega(60))= round((2+1+1)/3)=1.

36 is in A067340. 12 and 60 are in A070011.

MATHEMATICA

Table[Round[PrimeOmega[n]/PrimeNu[n]], {n, 2, 50}] (* G. C. Greubel, May 08 2017 *)

PROG

(PARI) v=[]; for(n=2, 150, v=concat(v, round(bigomega(n)/omega(n)))); v

CROSSREFS

Cf. A001221 (omega(n)), A001222 (bigomega(n)), A067340 (ratio is integer before rounding), A070011 (ratio is not an integer), A070012 (floor of ratio), A070014 (ceiling of ratio), A046660 (bigomega(n)-omega(n)).

Sequence in context: A302035 A307907 A088388 * A070014 A051903 A324912

Adjacent sequences:  A070010 A070011 A070012 * A070014 A070015 A070016

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Apr 11 2002

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 November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)