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A369643
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a(n) = 1 if n' / gcd(n,n') is a multiple of 3, otherwise 0. Here n' stands for the arithmetic derivative of n, A003415.
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5
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1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0
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OFFSET
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1
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COMMENTS
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a(n) = 1 if numerator of Sum(e/p: n=Product(p^e)) is of the form 3k, and 0 if it is not.
Question: Does this sequence have an asymptotic mean? Partial sums for range [1..10^n-1], for n=1..10 are: 2, 19, 208, 2196, 22346, 225544, 2267048, 22752664, 228098405, 2285194569.
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LINKS
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FORMULA
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a(n) = [A083345(n) == 0 (mod 3)], where [ ] is the Iverson bracket.
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PROG
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(PARI)
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
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CROSSREFS
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Characteristic function of A369644.
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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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