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A070012
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Floor of number of prime factors of n divided by the number of n's distinct prime factors.
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4
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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
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OFFSET
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2,3
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COMMENTS
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a(n) is the integer part of the average of the exponents in the prime factorization of n.
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LINKS
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Table of n, a(n) for n=2..106.
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FORMULA
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a(n) = floor(bigomega(n)/omega(n)) for n>=2.
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EXAMPLE
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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.
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MATHEMATICA
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A070012[n_]:=Floor[PrimeOmega[n]/PrimeNu[n]]; Array[A070012, 100]
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PROG
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(PARI) v=[]; for(n=2, 150, v=concat(v, (bigomega(n)\omega(n)))); v In PARI, j\k using the "\" operator for integers j, k is equivalent to floor(j/k).
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CROSSREFS
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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: A158378 A052409 A051904 * A071178 A072776 A077481
Adjacent sequences: A070009 A070010 A070011 * A070013 A070014 A070015
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd, Apr 11 2002
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STATUS
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approved
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