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A212645
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a(n) = number of excess prime divisors of A181800(n) (n-th powerful number that is the first integer of its prime signature).
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2
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0, 1, 2, 3, 4, 2, 5, 3, 6, 4, 4, 7, 5, 5, 8, 6, 6, 3, 9, 7, 6, 7, 4, 10, 8, 7, 8, 5, 11, 9, 8, 5, 9, 6, 8, 12, 10, 9, 6, 10, 7, 9, 13, 11, 10, 7, 6, 11, 8, 10, 7, 14, 12, 11, 8, 4, 10, 7, 12, 9, 11, 8, 15, 13, 12, 9, 5, 11, 8, 13, 10, 12, 9, 16, 14, 8, 13, 10
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OFFSET
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1,3
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COMMENTS
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The excess of n, or A046660(n), is a function of the second signature of n (cf. A212172). Since A181800 gives the first integer of each second signature, this sequence gives the value of A046660 for each second signature in order of its first appearance. Each nonnegative integer n occurs A000041(n) times in the sequence.
a(n) is also the number of prime factors of A212638(n), counted with multiplicity.
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LINKS
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FORMULA
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EXAMPLE
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36 (2^2*3^2, or 2*2*3*3) has 4 prime factors when repetitions are counted, but only 2 distinct prime factors. Therefore, its "excess" as defined in A046660 is (4-2) = 2. Since 36 = A181800(6), a(6) = 2.
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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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