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

0,1

Links

Table of n, a(n) for n=0..105.

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

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.

Example

0.823265208269485020156816453947090406301273270321142250892524579208530395971755...

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

Crossrefs

Cf. A061502, A092742, A245074, A319091.

Sequence in context: A114314 A013662 A291362 * A222225 A140244 A160105

Adjacent sequences: A319087 A319088 A319089 * A319091 A319092 A319093

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 10 2018

Status

approved