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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. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A193968 A153840 A198351 * A194474 A316161 A153349

Adjacent sequences:  A245071 A245072 A245073 * A245075 A245076 A245077

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jul 11 2014

STATUS

approved

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Last modified September 19 22:06 EDT 2021. Contains 347576 sequences. (Running on oeis4.)