cp's OEIS Frontend

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

%I A070012 #19 Jan 10 2025 10:08:20
%S A070012 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,
%T A070012 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,
%U A070012 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
%N A070012 Floor of number of prime factors of n divided by the number of n's distinct prime factors.
%C A070012 a(n) is the integer part of the average of the exponents in the prime factorization of n.
%H A070012 G. C. Greubel, <a href="/A070012/b070012.txt">Table of n, a(n) for n = 2..5000</a>
%F A070012 a(n) = floor(bigomega(n)/omega(n)) for n>=2.
%e A070012 a(12)=1 because 12=2^2 * 3^1 and floor(bigomega(12)/omega(12)) = floor((2+1)/2) = 1.
%e A070012 a(36)=2 because 36=2^2 * 3^2 and floor(bigomega(36)/omega(36)) = floor((2+2)/2) = 2.
%e A070012 a(60)=1 because 60=2^2 * 3^1 * 5^1 and floor(bigomega(60)/omega(60)) = floor((2+1+1)/3) = 1.
%e A070012 36 is in A067340. 12 and 60 are in A070011.
%t A070012 A070012[n_]:=Floor[PrimeOmega[n]/PrimeNu[n]];Array[A070012,100]
%o A070012 (PARI) v=[]; for(n=2,150,v=concat(v,(bigomega(n)\omega(n)))); v
%Y A070012 Cf. A001221 (omega(n)), A001222 (bigomega(n)), A067340 (ratio is an integer before floor applied), A070011 (ratio is not an integer), A070013 (ratio rounded), A070014 (ceiling of ratio), A046660 (bigomega(n)-omega(n)).
%K A070012 nonn
%O A070012 2,3
%A A070012 _Rick L. Shepherd_, Apr 11 2002