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A065332
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3-smooth numbers in their natural position, gaps filled with 0.
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4
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1, 2, 3, 4, 0, 6, 0, 8, 9, 0, 0, 12, 0, 0, 0, 16, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 27, 0, 0, 0, 0, 32, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = if A065330(n) = 1 then n else 0.
Multiplicative with a(p^e) = p^e if p <= 3, and 0 otherwise.
Dirichlet g.f.: 6^s / ((2^s-2)*(3^s-3)).
Sum_(k=1..n} a(k) ~ (n/(log(2)*log(3))) * (log(n) + log(6)/2 - 1). (End)
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MATHEMATICA
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smooth3Q[n_] := n == 2^IntegerExponent[n, 2]*3^IntegerExponent[n, 3];
a[n_] := n Boole[smooth3Q[n]];
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PROG
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(PARI) a(n) = if(n >> valuation(n, 2) == 3^valuation(n, 3), n, 0); \\ Amiram Eldar, Sep 16 2023
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CROSSREFS
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KEYWORD
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mult,nonn,easy
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AUTHOR
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STATUS
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approved
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