|
%I #17 Sep 10 2018 10:38:49
%S 7,4,4,3,4,1,2,7,6,3,9,1,4,5,6,6,4,0,4,3,9,0,0,6,0,3,6,7,8,5,6,9,4,6,
%T 1,5,6,9,1,3,7,7,8,0,8,8,3,9,4,2,7,0,4,7,5,8,5,2,9,2,0,9,4,8,7,7,3,6,
%U 4,0,8,4,0,1,4,8,2,5,8,4,1,6,2,0,5,7,0,1,9,8,7,4,8,8,7,1,8,5,0,0,9,4,5
%N Decimal expansion of B, the coefficient of n*log(n)^2 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.
%C The coefficient of n*log(n)^3 in the same asymptotic formula is A = 1/Pi^2.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section Sierpinski's Constant, p. 124.
%H Adrian W. Dudek, <a href="http://arxiv.org/abs/1401.1514">An Elementary Proof of an Asymptotic Formula of Ramanujan</a>, arXiv:1401.1514 [math.NT], 2014.
%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 B = (12*gamma - 3)/Pi^2 - (36/Pi^4)*zeta'(2).
%e 0.744341276391456640439006036785694615691377808839427047585292094877364...
%t B = (12*EulerGamma - 3)/Pi^2 - (36/Pi^4)*Zeta'[2]; RealDigits[B, 10, 103] // First
%Y Cf. A061502, A073002, A092742, A319090, A319091.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Jul 11 2014
|
