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%I #13 May 09 2017 00:09:26
%S 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,
%T 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,
%U 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
%N Number of prime factors of n divided by the number of n's distinct prime factors (rounded).
%C a(n) is the rounded average of the exponents in the prime factorization of n.
%H G. C. Greubel, <a href="/A070013/b070013.txt">Table of n, a(n) for n = 2..1000</a>
%F a(n) = round(bigomega(n)/omega(n)) for n>=2.
%e a(12)=2 because 12=2^2 * 3^1 and round(bigomega(12)/omega(12))=round((2+1)/2)=2.
%e a(36)=2 because 36=2^2 * 3^2 and round(bigomega(36)/omega(36))=round((2+2)/2)=2.
%e a(60)=1 because 60=2^2 * 3^1 * 5^1 and round(bigomega(60)/omega(60))= round((2+1+1)/3)=1.
%e 36 is in A067340. 12 and 60 are in A070011.
%t Table[Round[PrimeOmega[n]/PrimeNu[n]], {n, 2, 50}] (* _G. C. Greubel_, May 08 2017 *)
%o (PARI) v=[]; for(n=2,150,v=concat(v,round(bigomega(n)/omega(n)))); v
%Y 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)).
%K nonn
%O 2,3
%A _Rick L. Shepherd_, Apr 11 2002
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