A245074 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.

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, 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, 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

Offset

0,1

Comments

The coefficient of n*log(n)^3 in the same asymptotic formula is A = 1/Pi^2.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section Sierpinski's Constant, p. 124.

Links

Table of n, a(n) for n=0..102.

Adrian W. Dudek, An Elementary Proof of an Asymptotic Formula of Ramanujan, arXiv:1401.1514 [math.NT], 2014.

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

Formula

B = (12*gamma - 3)/Pi^2 - (36/Pi^4)*zeta'(2).

Example

0.744341276391456640439006036785694615691377808839427047585292094877364...

Mathematica

B = (12*EulerGamma - 3)/Pi^2 - (36/Pi^4)*Zeta'[2]; RealDigits[B, 10, 103] // First

Crossrefs

Cf. A061502, A073002, A092742, A319090, A319091.

Sequence in context: A153840 A198351 A354249 * A194474 A348736 A316161

Adjacent sequences: A245071 A245072 A245073 * A245075 A245076 A245077

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 11 2014

Status

approved