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%I #20 Sep 18 2022 12:36:57
%S 1,2,5,3,13,15,47,25,13,55,281,74,301,311,637,163,1319,453,4117,4207,
%T 4267,4339,48089,49079,9895,10027,10115,10247,72125,73511,369403,
%U 93217,9391,75821,76283,77207,77515,78131,78593,39643,49727,100609,100939,25408,204419
%N Numerator of Sum_{k=1..n} 1/phi(k).
%D József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Section I.27, page 29.
%H Robert Israel, <a href="/A028415/b028415.txt">Table of n, a(n) for n = 1..10000</a>
%H R. Sitaramachandrarao, <a href="https://www.jstor.org/stable/44236939">On an error term of Landau - II</a>, The Rocky Mountain Journal of Mathematics, Vol. 15, No. 2 (1985), pp. 579-588.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientSummatoryFunction.html">Totient Summatory Function</a>.
%F 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
%e 1, 2, 5/2, 3, 13/4, 15/4, 47/12, 25/6, 13/3, 55/12, 281/60, 74/15, ...
%p map(numer, ListTools:-PartialSums(map(1/numtheory:-phi, [$1..10000]))); # _Robert Israel_, Apr 16 2019
%t Numerator[Table[Sum[1/EulerPhi[k],{k,n}],{n,50}]] (* _Harvey P. Dale_, Aug 24 2012 *)
%o (PARI) a(n) = numerator(sum(k=1, n, 1/eulerphi(k))); \\ _Michel Marcus_, Sep 18 2022
%Y Cf. A000010, A048049 (denominators).
%Y Cf. A001620, A085609, A082695.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Jun 28 2002
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