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A028235
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If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j (the denominator of this sum is A007947).
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6
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0, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 5, 1, 9, 8, 1, 1, 5, 1, 7, 10, 13, 1, 5, 1, 15, 1, 9, 1, 31, 1, 1, 14, 19, 12, 5, 1, 21, 16, 7, 1, 41, 1, 13, 8, 25, 1, 5, 1, 7, 20, 15, 1, 5, 16, 9, 22, 31, 1, 31, 1, 33, 10, 1, 18, 61, 1, 19, 26, 59, 1, 5, 1, 39, 8, 21, 18, 71, 1, 7, 1, 43, 1, 41, 22, 45, 32
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OFFSET
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1,6
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COMMENTS
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LINKS
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FORMULA
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Fraction is additive with a(p^e) = 1/p.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A007947(k) = Sum_{p prime} 1/p^2 = 0.452247... (A085548). - Amiram Eldar, Sep 29 2023
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EXAMPLE
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Fractions begin with 0, 1/2, 1/3, 1/2, 1/5, 5/6, 1/7, 1/2, 1/3, 7/10, 1/11, 5/6, ...
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MATHEMATICA
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a[1] = 0; a[n_] := 1/FactorInteger[n][[All, 1]] // Total // Numerator;
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PROG
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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