A098468 Decimal expansion of constant A*B in the asymptotic expression of the summatory function Sum_{n=1..N} (1/phi(n)) as A(log(N)+B) + O(log(N)/N).

0, 6, 0, 5, 7, 4, 2, 2, 9, 4, 8, 6, 3, 0, 5, 7, 3, 2, 1, 6, 0, 9, 7, 4, 4, 0, 1, 1, 6, 6, 3, 1, 3, 8, 4, 0, 3, 5, 4, 9, 7, 2, 2, 8, 4, 0, 8, 8, 2, 9, 8, 9, 2, 8, 1, 1, 5, 1, 2, 2, 4, 4, 8, 5, 6, 0, 9, 3, 4, 9, 8, 5, 5, 9, 0, 1, 8, 6, 4, 9, 1, 3, 1, 2, 3, 9, 2, 9, 8, 1, 5

Offset

0,2

Comments

B equals EulerGamma - A085609.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.7 Euler totient constants, p. 116.

Links

Table of n, a(n) for n=0..90.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 52 (Z1*(gamma-Z2)).

Eric Weisstein's World of Mathematics, Totient Summatory Function

Formula

Sum_{n=1..N} 1/phi(n) = A*(log(N)+B) + O(log(N)/N). - Jean-François Alcover, Apr 28 2018

Example

B = -0.0605742294.../A, where A is A082695.

Mathematica

(* Using S. Finch's notation *)
digits = 102;
A = Zeta[2]*Zeta[3]/Zeta[6];
S = Sum[Switch[Mod[k, 6], 0, 1, 1, 0, 2, -1, 3, -1, 4, 0, 5, 1]*PrimeZetaP'[k], {k, 2, 400}] // N[#, digits+40]&;
B = EulerGamma - S;
AB = A*B;
Join[{0}, RealDigits[AB, 10, digits][[1]]] (* Jean-François Alcover, Apr 28 2018 *)

Crossrefs

Cf. A082695, A085609.

Sequence in context: A348359 A153754 A096410 * A196625 A343948 A195368

Adjacent sequences: A098465 A098466 A098467 * A098469 A098470 A098471

Keyword

nonn,cons,hard

Author

Eric W. Weisstein, Sep 09 2004

Extensions

More digits with the aid of A085609 and A082695 from R. J. Mathar, Jul 28 2010

More digits with the aid of A085609 and A082695 from Vaclav Kotesovec, Feb 17 2015

Status

approved