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A360616
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Half the number of prime factors of n (counted with multiplicity, A001222), rounded down.
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11
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0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 1, 0, 2, 1, 1, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 3, 1, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 2, 1, 1, 1
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OFFSET
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1,16
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LINKS
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EXAMPLE
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The prime indices of 378 are {1,2,2,2,4}, so a(378) = floor(5/2) = 2.
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MATHEMATICA
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Table[Floor[PrimeOmega[n]/2], {n, 100}]
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CROSSREFS
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Positions of 0's are 1 and A000040.
Positions of first appearances are A000302 = 2^(2k) for k >= 0.
Rounding up instead of down gives A360617.
First for prime indices, second for partitions, third for prime factors:
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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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