OFFSET
1,2
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Section I.27, page 29.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
R. Sitaramachandrarao, On an error term of Landau - II, The Rocky Mountain Journal of Mathematics, Vol. 15, No. 2 (1985), pp. 579-588.
Eric Weisstein's World of Mathematics, Totient Summatory Function.
FORMULA
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
EXAMPLE
1, 2, 5/2, 3, 13/4, 15/4, 47/12, 25/6, 13/3, 55/12, 281/60, 74/15, ...
MAPLE
map(numer, ListTools:-PartialSums(map(1/numtheory:-phi, [$1..10000]))); # Robert Israel, Apr 16 2019
MATHEMATICA
Numerator[Table[Sum[1/EulerPhi[k], {k, n}], {n, 50}]] (* Harvey P. Dale, Aug 24 2012 *)
PROG
(PARI) a(n) = numerator(sum(k=1, n, 1/eulerphi(k))); \\ Michel Marcus, Sep 18 2022
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jun 28 2002
STATUS
approved