A319090 Decimal expansion of C, the coefficient of n*log(n) in the asymptotic formula of Ramanujan for Sum_{k=1..n} (d(k)^2), where d(k) is the number of distinct divisors of k.

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

Offset: 0

Author

Vaclav Kotesovec, Sep 10 2018

Keywords

• nonn
• cons

Examples

			0.823265208269485020156816453947090406301273270321142250892524579208530395971755...
		

Links

• Ramanujan's Papers, Some formulas in the analytic theory of numbers Messenger of Mathematics, XLV, 1916, 81-84, Formula (3).

Crossrefs

Cf. A061502, A092742, A245074, A319091.

Programs

Mathematica

36*EulerGamma^2/Pi^2 - (288*Zeta'[2]/Pi^4 + 24/Pi^2)*EulerGamma + (864*Zeta'[2]^2/Pi^6 + 72*Zeta'[2]/Pi^4 - 72/Pi^4*Zeta''[2] + 6/Pi^2) - 24*StieltjesGamma[1]/Pi^2

Formula

C = 36*gamma^2/Pi^2 - (288*z1/Pi^4 + 24/Pi^2)*gamma + (864*z1^2/Pi^6 + 72*z1/Pi^4 - 72/Pi^4*z2 + 6/Pi^2) - 24*g1/Pi^2, where gamma is the Euler-Mascheroni constant A001620, z1 = Zeta'(2) = A073002, z2 = Zeta''(2) = A201994 and g1 is the first Stieltjes constant, see A082633.