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A327486
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Product of Omegas of positive integers from 2 to n.
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6
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1, 1, 1, 2, 2, 4, 4, 12, 24, 48, 48, 144, 144, 288, 576, 2304, 2304, 6912, 6912, 20736, 41472, 82944, 82944, 331776, 663552, 1327104, 3981312, 11943936, 11943936, 35831808, 35831808, 179159040, 358318080, 716636160, 1433272320, 5733089280, 5733089280, 11466178560
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OFFSET
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1,4
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COMMENTS
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Omega(n) (A001222) is the number of prime factors of n, counted with multiplicity.
Also the number of ways to choose a prime factor, counting multiplicity, of each positive integer from 2 to n.
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LINKS
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FORMULA
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EXAMPLE
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We have a(8) = 1 * 1 * 2 * 1 * 2 * 1 * 3 = 12.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, n,
numtheory[bigomega](n)*a(n-1))
end:
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MATHEMATICA
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Table[Product[PrimeOmega[k], {k, 2, n}], {n, 30}]
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PROG
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(PARI) a(n) = prod(k=2, n, bigomega(k)); \\ Michel Marcus, Sep 29 2019
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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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