VOOZH about

URL: https://oeis.org/A068885

⇱ A068885 - OEIS

login
A068885
Numerator of Sum_{k=1..n} k/phi(k).
3
1, 3, 9, 13, 31, 43, 143, 167, 185, 215, 1141, 1321, 231, 763, 3277, 3517, 7289, 8009, 24787, 26587, 27847, 29431, 332021, 355781, 365681, 382841, 394721, 413201, 2949827, 3157727, 643003, 665179, 3417371, 3535181, 3616031, 3782351, 1279777, 3956371, 4046461
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
R. Sitaramachandrarao, On an error term of Landau - II, The Rocky Mountain Journal of Mathematics, Vol. 15, No. 2 (1985), pp. 579-588.
FORMULA
a(n)/A069947(n) ~ c * n - log(n)/2 + O(log(n)^(2/3)), where c = zeta(2)*zeta(3)/zeta(6) (A082695) (Sitaramachandrarao, 1985). - Amiram Eldar, Sep 18 2022
EXAMPLE
1, 3, 9/2, 13/2, 31/4, 43/4, 143/12, 167/12, 185/12, ...
MATHEMATICA
Numerator @ Accumulate @ Table[k/EulerPhi[k], {k, 1, 40}] (* Amiram Eldar, Sep 18 2022 *)
PROG
(PARI) a(n) = numerator(sum(k=1, n, k/eulerphi(k))); \\ Michel Marcus, Sep 18 2022
CROSSREFS
Cf. A069947 (denominators), A000010, A028415, A048049, A082695.
Sequence in context: A215443 A304664 A385115 * A305644 A316920 A018292
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jun 28 2002
STATUS
approved