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

Author

Jean-François Alcover, Jul 11 2014

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			0.744341276391456640439006036785694615691377808839427047585292094877364...
		

References

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

Links

• 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).

Crossrefs

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

Programs

Mathematica

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

PARI

(4*Euler-1)/(2*zeta(2)) - zeta'(2)/zeta(2)^2 \\ Amiram Eldar, Apr 27 2025

Formula

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