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A158584
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The integer part of the geometric mean of the prime factors of n with multiplicity.
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0
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2, 3, 1, 5, 2, 7, 1, 3, 3, 11, 2, 13, 3, 3, 1, 17, 2, 19, 2, 4, 4, 23, 2, 4, 5, 3, 3, 29, 3, 31, 1, 5, 5, 5, 2, 37, 6, 6, 2, 41, 3, 43, 3, 3, 6, 47, 2, 7, 3, 7, 3, 53, 2, 7, 2, 7, 7, 59, 2, 61, 7, 3, 1, 8, 4, 67, 4, 8, 4, 71, 2, 73, 8, 4, 4, 8, 4, 79, 2, 3, 9, 83, 3, 9, 9, 9, 3, 89, 3, 9, 4, 9, 9, 9, 2, 97
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| We do not begin with the unit 1 because it has no prime factors. Conjecture:
The sequence contains the set of prime numbers more than once.
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FORMULA
| The geometric mean is the n-th root of the product of n numbers.
Gm = (a(1)*a(2)*...*a(n))^(1/n).
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EXAMPLE
| 12=2*2*3 has 3 factors; 12^(1/3) = 2.289428... so 2 is in the 11th position in
the sequence.
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PROG
| (PARI) g(n) = for(x=2, n, print1(floor(x^(1/bigomega(x)))", "))
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CROSSREFS
| Sequence in context: A055023 A126773 A134194 * A086112 A138798 A134734
Adjacent sequences: A158581 A158582 A158583 * A158585 A158586 A158587
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Mar 21 2009
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