A068885 Numerator of Sum_{k=1..n} k/phi(k).

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

Author

N. J. A. Sloane, Jun 28 2002

Keywords

• nonn
• frac

Examples

			1, 3, 9/2, 13/2, 31/4, 43/4, 143/12, 167/12, 185/12, ...
		

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

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• R. Sitaramachandrarao, On an error term of Landau - II, The Rocky Mountain Journal of Mathematics, Vol. 15, No. 2 (1985), pp. 579-588.

Crossrefs

Cf. A069947 (denominators), A000010, A028415, A048049, A082695.

Programs

Mathematica

Numerator @ Accumulate @ Table[k/EulerPhi[k], {k, 1, 40}] (* Amiram Eldar, Sep 18 2022 *)

PARI

a(n) = numerator(sum(k=1, n, k/eulerphi(k))); \\ Michel Marcus, Sep 18 2022

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