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A074467
Least k such that sum_{i=1..k} 1/phi(i) >= n.
1
1, 2, 4, 8, 13, 22, 38, 63, 105, 177, 296, 495, 828, 1386, 2318, 3879, 6489, 10854, 18158, 30375, 50811, 84998, 142187, 237853, 397885, 665589, 1113411, 1862534, 3115683, 5211973, 8718687, 14584783, 24397699, 40812930, 68272636, 114207749, 191048868, 319590137
OFFSET
1,2
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 177, p. 55, Ellipses, Paris 2008.
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.
LINKS
H. L. Montgomery, Primes in arithmetic progressions, Michigan Math. J. 17:1 (1970), pp. 33-39. [alternate link]
FORMULA
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
MATHEMATICA
{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}]
PROG
(PARI) a(n)=my(s, k); while(s<n, s+=1./eulerphi(k++)); k \\ Charles R Greathouse IV, Jan 29 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 29 2002
EXTENSIONS
More terms from Ryan Propper, Jul 09 2005
a(32)-a(38) from Donovan Johnson, Aug 21 2011
STATUS
approved