A070013 Number of prime factors of n divided by the number of n's distinct prime factors (rounded).

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

Offset: 2

Author

Rick L. Shepherd, Apr 11 2002

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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