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%I #21 Oct 15 2013 22:31:29
%S 1,2,4,8,13,22,38,63,105,177,296,495,828,1386,2318,3879,6489,10854,
%T 18158,30375,50811,84998,142187,237853,397885,665589,1113411,1862534,
%U 3115683,5211973,8718687,14584783,24397699,40812930,68272636,114207749,191048868,319590137
%N Least k such that sum_{i=1..k} 1/phi(i) >= n.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 177, p. 55, Ellipses, Paris 2008.
%D E. Landau, Uber die Zahlentheoretische Function ϕ(n) und ihre Beziehung zum Goldbachschen satz, Nachrichten der Koniglichten Gesel lschaft der Wissenschaften zu Göttingen mathematisch Physikalische klasse, Jahrgang (1900), pp. 177-186.
%H H. L. Montgomery, <a href="http://projecteuclid.org/euclid.mmj/1029000373">Primes in arithmetic progressions</a>, Michigan Math. J. 17:1 (1970), pp. 33-39. [<a href="http://www.williams.edu/go/math/sjmiller/public_html/ntrmt10/handouts/primes/Montgomery_ErrorPrimeSums1970.pdf">alternate link</a>]
%F a(n) ~ k exp(cn) for c = zeta(6)/zeta(2)/zeta(3) = A068468 and k = exp(-gamma + A085609) = 1.0316567993311528...; see Montgomery or Koninck. - _Charles R Greathouse IV_, Jan 29 2013
%t {s=0, s1=0}; Do[s=s+(1/EulerPhi[n]); If[Greater[Floor[s], s1], s1=Floor[s]; Print[{n, Floor[s]}]], {n, 1, 1000000}]
%o (PARI) a(n)=my(s,k);while(s<n, s+=1./eulerphi(k++)); k \\ _Charles R Greathouse IV_, Jan 29 2013
%Y Cf. A002387, A004080, A046024, A074631, A074633.
%K nonn
%O 1,2
%A _Labos Elemer_, Aug 29 2002
%E More terms from _Ryan Propper_, Jul 09 2005
%E a(32)-a(38) from _Donovan Johnson_, Aug 21 2011
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