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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.
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%I #8 Sep 10 2018 12:41:30

%S 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,

%T 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,

%U 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

%N 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.

%H Ramanujan's Papers, <a href="http://ramanujan.sirinudi.org/Volumes/published/ram17.html">Some formulas in the analytic theory of numbers</a> Messenger of Mathematics, XLV, 1916, 81-84, Formula (3).

%F 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.

%e 0.823265208269485020156816453947090406301273270321142250892524579208530395971755...

%t 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

%Y Cf. A061502, A092742, A245074, A319091.

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, Sep 10 2018