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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
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
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
Sequence in context: A348359 A153754 A096410 * A196625 A343948 A195368
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