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A165743
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The greatest common divisor of n and 210.
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1
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1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 1, 6, 1, 14, 15, 2, 1, 6, 1, 10, 21, 2, 1, 6, 5, 2, 3, 14, 1, 30, 1, 2, 3, 2, 35, 6, 1, 2, 3, 10, 1, 42, 1, 2, 15, 2, 1, 6, 7, 10, 3, 2, 1, 6, 5, 14, 3, 2, 1, 30, 1, 2, 21, 2, 5, 6, 1, 2, 3, 70, 1, 6, 1, 2, 15, 2, 7, 6, 1, 10, 3, 2, 1, 42, 5, 2, 3, 2, 1, 30, 7, 2, 3, 2, 5, 6
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OFFSET
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1,2
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COMMENTS
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Note: 210 = 2*3*5*7, the product of the first four primes.
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LINKS
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FORMULA
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a(n) = gcd(n, 210).
Multiplicative with a(p^e) = p if p <= 7, and 1 otherwise.
Dirichlet g.f.: zeta(s) * (1 + 1/2^s) * (1 + 2/3^s) * (1 + 4/5^s) * (1 + 6/7^s).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 117/14. (End)
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MAPLE
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MATHEMATICA
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a[n_] := GCD[n, 210]; Array[a, 100] (* Amiram Eldar, Sep 16 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Mick Purcell (mickpurcell(AT)gmail.com), Sep 26 2009
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EXTENSIONS
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STATUS
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approved
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