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A070013
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Number of prime factors of n divided by the number of n's distinct prime factors (rounded).
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6
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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
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OFFSET
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2,3
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COMMENTS
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a(n) is the rounded average of the exponents in the prime factorization of n.
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LINKS
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FORMULA
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a(n) = round(bigomega(n)/omega(n)) for n>=2.
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EXAMPLE
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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.
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MATHEMATICA
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Table[Round[PrimeOmega[n]/PrimeNu[n]], {n, 2, 50}] (* G. C. Greubel, May 08 2017 *)
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PROG
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(PARI) v=[]; for(n=2, 150, v=concat(v, round(bigomega(n)/omega(n)))); v
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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