login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A242051 Decimal expansion of B, a constant appearing in the asymptotic number of integers the prime factorization of which has decreasing exponents. 1

%I #18 Jan 17 2020 05:41:02

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

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

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

%N Decimal expansion of B, a constant appearing in the asymptotic number of integers the prime factorization of which has decreasing exponents.

%H G. C. Greubel, <a href="/A242051/b242051.txt">Table of n, a(n) for n = 1..10000</a>

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 9.

%H L. B. Richmond, <a href="https://doi.org/10.1016/0022-314X(76)90085-8">Asymptotic results for partitions (I) and the distribution of certain integers</a>, Journal of Number Theory 8, 372-389 (1976) p. 388.

%F B = -integral_{y>0} log(1-e^(-y))*log(y) dy = zeta'(2) - (Pi^2/6)*gamma.

%t RealDigits[Zeta'[2] - (Pi^2/6)*EulerGamma, 10, 105] // First

%o (PARI) default(realprecision, 100); zeta'(2) - zeta(2)*Euler \\ _G. C. Greubel_, Sep 06 2018

%Y Cf. A001620, A073002.

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Aug 13 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 22:19 EDT 2024. Contains 374461 sequences. (Running on oeis4.)