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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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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| a(n) is the rounded average of the exponents in the prime factorization of n.
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FORMULA
| a(n) = round(bigomega(n)/omega(n)) for n>=2.
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EXAMPLE
| 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. 36 is in A067340. 12 and 60 are in A070011.
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PROG
| (PARI) v=[]; for(n=2, 150, v=concat(v, round(bigomega(n)/omega(n)))); v
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CROSSREFS
| 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)).
Sequence in context: A067029 A087179 A088388 * A070014 A051903 A157754
Adjacent sequences: A070010 A070011 A070012 * A070014 A070015 A070016
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Apr 11 2002
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