A246749 Decimal expansion of F'(rho), an auxiliary constant associated with the asymptotic number of values of the Euler totient function less than a given number, where the function F and the constant rho are defined in A246746.

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

Offset: 1

Author

Jean-François Alcover, Sep 02 2014

Keywords

• nonn
• cons

Examples

			5.6977589342301926757529137046852478978581019821783573593459567...
		

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 16.
• Kevin Ford, The distribution of Totients

Crossrefs

Cf. A246746.

Programs

Mathematica

digits = 101; F[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*x^k, {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; F'[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*k*x^(k - 1), {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; rho = x /. FindRoot[F[x] == 1, {x, 5/10, 6/10}, WorkingPrecision -> digits + 10]; RealDigits[F'[rho], 10, digits] // First

Formula

Let F(x) = sum_{k >= 1} ((k+1)*log(k+1) - k*log(k) - 1)*x^k.

F'(rho), where rho is the unique solution on [0,1) of F(rho)=1,