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A099812
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Number of distinct primes dividing 2n (i.e., omega(2n)).
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3
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1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 1, 3, 3, 2, 2, 3, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 4
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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a(6)=2 because 12 = 2*2*3 has 2 distinct prime divisors;
a(15)=3 because 30 = 2*3*5 has 3 distinct prime divisors.
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MAPLE
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with(numtheory): omega:=proc(n) local div, A, j: div:=divisors(n): A:={}: for j from 1 to tau(n) do if isprime(div[j])=true then A:=A union {div[j]} else A:=A fi od: nops(A) end: seq(omega(2*n), n=1..130); # Emeric Deutsch, Mar 10 2005
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MATHEMATICA
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PROG
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(PARI) for(n=1, 50, print1(omega(2*n), ", ")) \\ G. C. Greubel, May 21 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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