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A028415
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Numerator of Sum_{k=1..n} 1/phi(k).
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10
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1, 2, 5, 3, 13, 15, 47, 25, 13, 55, 281, 74, 301, 311, 637, 163, 1319, 453, 4117, 4207, 4267, 4339, 48089, 49079, 9895, 10027, 10115, 10247, 72125, 73511, 369403, 93217, 9391, 75821, 76283, 77207, 77515, 78131, 78593, 39643, 49727, 100609, 100939, 25408, 204419
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OFFSET
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1,2
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REFERENCES
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József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Section I.27, page 29.
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LINKS
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FORMULA
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a(n)/A048049(n) ~ c * (log(n) + gamma - s) + O(log(n)^(2/3)/n), where c = zeta(2)*zeta(3)/zeta(6) (A082695), gamma is Euler's constant (A001620), and s = Sum_{p prime} log(p)/(p^2-p+1) (A085609) (Sitaramachandrarao, 1985). - Amiram Eldar, Sep 18 2022
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EXAMPLE
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1, 2, 5/2, 3, 13/4, 15/4, 47/12, 25/6, 13/3, 55/12, 281/60, 74/15, ...
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MAPLE
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map(numer, ListTools:-PartialSums(map(1/numtheory:-phi, [$1..10000]))); # Robert Israel, Apr 16 2019
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MATHEMATICA
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Numerator[Table[Sum[1/EulerPhi[k], {k, n}], {n, 50}]] (* Harvey P. Dale, Aug 24 2012 *)
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PROG
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(PARI) a(n) = numerator(sum(k=1, n, 1/eulerphi(k))); \\ Michel Marcus, Sep 18 2022
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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