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A071708
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Numerator of Sum_{k=1..n} phi(k)/k.
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4
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1, 3, 13, 8, 52, 19, 163, 361, 1223, 1307, 16477, 5749, 83977, 88267, 280817, 147916, 2754812, 2839897, 58552633, 60492571, 63263911, 65468386, 1612469468, 549883871, 579629587, 596790577, 1864736021, 1912541636, 58587007624, 59449633388, 1939984033478
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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.24, page 27.
Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Berlin, 1963.
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LINKS
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FORMULA
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Also numerator of Sum_{i=1..n} (mu(i)/i)*floor(n/i). - Ridouane Oudra, Nov 26 2019
a(n)/A072155(n) ~ (6/Pi^2) * n + O(log(n)^(2/3)*log(log(n))^(4/3)). - Amiram Eldar, Sep 18 2022
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EXAMPLE
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1, 3/2, 13/6, 8/3, 52/15, 19/5, 163/35, 361/70, 1223/210, ...
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MAPLE
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with(numtheory); seq(numer(add(phi(k)/k, k = 1..n)), n = 1..35); # G. C. Greubel, Aug 25 2019
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MATHEMATICA
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Table[Sum[EulerPhi[k]/k, {k, n}], {n, 35}]//Numerator (* G. C. Greubel, Aug 25 2019 *)
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PROG
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(PARI) a(n) = numerator(sum(k=1, n, eulerphi(k)/k));
(Magma) [Numerator( &+[EulerPhi(k)/k: k in [1..n]] ): n in [1..35]]; // G. C. Greubel, Aug 25 2019
(Sage) [numerator( sum(euler_phi(k)/k for k in (1..n)) ) for n in (1..35)] # G. C. Greubel, Aug 25 2019
(GAP) List([1..35], n-> NumeratorRat( Sum([1..n], k-> Phi(k)/k) ) ); # G. C. Greubel, Aug 25 2019
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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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