A070012 Floor of number of prime factors of n divided by the number of n's distinct prime factors.

1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1

Offset

2,3

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 2..5000

Formula

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

Example

a(12)=1 because 12=2^2 * 3^1 and floor(bigomega(12)/omega(12)) = floor((2+1)/2) = 1.
a(36)=2 because 36=2^2 * 3^2 and floor(bigomega(36)/omega(36)) = floor((2+2)/2) = 2.
a(60)=1 because 60=2^2 * 3^1 * 5^1 and floor(bigomega(60)/omega(60)) = floor((2+1+1)/3) = 1.
36 is in A067340. 12 and 60 are in A070011.

Mathematica

A070012[n_]:=Floor[PrimeOmega[n]/PrimeNu[n]]; Array[A070012, 100]

Prog

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

Crossrefs

Cf. A001221 (omega(n)), A001222 (bigomega(n)), A067340 (ratio is integer before floor applied), A070011 (ratio is not an integer), A070013 (ratio rounded), A070014 (ceiling of ratio), A046660 (bigomega(n)-omega(n)).

Sequence in context: A052409 A327503 A051904 * A375034 A373365 A071178

Adjacent sequences: A070009 A070010 A070011 * A070013 A070014 A070015

Keyword

nonn

Author

Rick L. Shepherd, Apr 11 2002

Status

approved