A378268 Decimal expansion of Sum_{p prime} log(1+1/p)/(p*(p-1)).

2, 6, 4, 8, 5, 9, 7, 2, 6, 6, 3, 1, 9, 0, 8, 0, 1, 9, 4, 5, 6, 0, 4, 5, 1, 5, 8, 5, 8, 6, 3, 2, 6, 4, 7, 2, 1, 7, 5, 4, 3, 8, 3, 7, 7, 1, 7, 0, 6, 9, 7, 7, 3, 6, 2, 1, 4, 4, 3, 2, 0, 1, 9, 5, 0, 1, 7, 0, 3, 3, 7, 9, 8, 9, 3, 0, 7, 8, 2, 9, 0, 9, 1, 5, 4, 0, 3, 8, 7, 3, 3, 8, 4, 7, 2, 4, 1, 4, 4, 3, 1, 2, 4, 1, 6

Offset

0,1

Comments

This constant appears in the formula for the average order of the logarithm of the divisor function: Sum_{k=1..n} log(d(n)) = log(2) * n * (log(log(n)) + B + C) + o(n), where d(n) = A000005(n), B is Mertens's constant (A077761), and C is this constant.

References

Jean-Marie De Koninck and Florian Luca, Analytic Number Theory: Exploring the Anatomy of Integers, American Mathematical Society, 2012, Problem 6.12, pp. 91 and 321.

Links

Table of n, a(n) for n=0..104.

Example

0.26485972663190801945604515858632647217543837717069...

Mathematica

$MaxExtraPrecision = 1000; With[{m = 1000}, c = CoefficientList[Series[Log[1 + x]*x/(1/x - 1), {x, 0, m}], x]; RealDigits[NSum[Indexed[c, n + 1]*PrimeZetaP[n], {n, 3, m}, NSumTerms -> m, WorkingPrecision -> m], 10, 120][[1]]]

Crossrefs

Cf. A000005, A077761.

Sequence in context: A088438 A259284 A345974 * A204906 A097265 A390007

Adjacent sequences: A378265 A378266 A378267 * A378269 A378270 A378271

Keyword

nonn,cons

Author

Amiram Eldar, Nov 21 2024

Status

approved