login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065465 Decimal expansion of product(1 - 1/(p^2*(p+1))), p prime >= 2). 2
8, 8, 1, 5, 1, 3, 8, 3, 9, 7, 2, 5, 1, 7, 0, 7, 7, 6, 9, 2, 8, 3, 9, 1, 8, 2, 2, 9, 0, 3, 2, 2, 7, 8, 4, 7, 1, 2, 9, 8, 6, 9, 2, 5, 7, 2, 0, 8, 0, 7, 6, 7, 3, 3, 6, 7, 0, 1, 6, 8, 5, 3, 5, 5, 4, 8, 6, 5, 7, 9, 0, 6, 3, 7, 9, 4, 1, 6, 9, 7, 4, 1, 0, 2, 2, 0, 4, 5, 5, 1, 7, 9, 7, 0, 2, 0, 9, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..97.

Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Math. Zeitschr. 74 (1960) 66-80.

S. R. Finch, Class number theory, page 7.

R. J. Mathar, Hardy-Littlewood constants embedded into infinite products..., arXiv:0903.2514 [math.NT], 2009-2011, Table 5, constant Q_1^(2).

G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]

Simon Plouffe, Generalized expansions of real numbers, 2006

Eric Weisstein's World of Mathematics, Quadratic Class Number Constant

Eric Weisstein's World of Mathematics, Prime Products

FORMULA

sum_{n>=1} phi(n)/(n*J(n)) = (this constant)*A013661 with phi()=A000010() and J() = A007434() [Cohen, Corollary 5.1.1], - R. J. Mathar, Apr 11 2011

EXAMPLE

0.88151383972517077692839182290...

MATHEMATICA

$MaxExtraPrecision = 1000; digits = 98; terms = 1000; LR = Join[{0, 0, 0}, LinearRecurrence[{-2, -1, 1, 1}, {-3, 4, -5, 3}, terms+10]]; r[n_Integer] := LR[[n]]; Exp[NSum[r[n]*PrimeZetaP[n-1]/(n-1), {n, 4, terms}, NSumTerms -> terms, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First (* Jean-Fran├žois Alcover, Apr 16 2016 *)

CROSSREFS

Cf. A078087.

Sequence in context: A091648 A135707 A021923 * A265308 A199597 A197848

Adjacent sequences:  A065462 A065463 A065464 * A065466 A065467 A065468

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane, Nov 19 2001

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 21:23 EST 2016. Contains 279011 sequences.