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!)
A218342 Decimal expansion of e^-gamma * Product_(1 - 1/(p^3 - p^2 - p + 1)) where the product is over all primes p. 4
3, 4, 5, 3, 7, 2, 0, 6, 4, 1, 0, 2, 9, 8, 6, 4, 8, 7, 6, 7, 3, 4, 9, 6, 8, 2, 7, 8, 9, 1, 0, 3, 3, 7, 1, 0, 7, 2, 0, 6, 6, 5, 6, 2, 5, 3, 8, 0, 4, 1, 5, 8, 7, 2, 0, 5, 6, 0, 0, 4, 8, 9, 6, 6, 2, 5, 2, 6, 5, 3, 1, 9, 5, 0, 2, 2, 5, 1, 8, 6, 6, 9, 4, 7, 9, 0, 9, 1, 1, 6, 1, 3, 9, 2, 2, 7, 6, 3, 9, 6, 9, 6, 4, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The average order of Carmichael's lambda function is x/log x * exp(B log log x/log log log x (1 + o(1))), where B is this constant. Under the GRH, the same applies to A036391(n)/n, the sum of the orders mod n of the numbers coprime to n divided by n.
LINKS
Paul Erdős, Carl Pomerance, and Eric Schmutz, Carmichael's lambda function, Acta Arithmetica 58 (1991), pp. 363-385.
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 156 (constant C9).
Sungjin Kim, On the order of 'a' modulo 'n' on average, International Journal of Number Theory, Vol. 12, No. 8 (2016), pp. 2073-2080; arXiv preprint, arXiv:1509.03768 [math.NT], 2015-2016.
Pär Kurlberg and Carl Pomerance, On a problem of Arnold: the average multiplicative order of a given integer, Algebra & Number Theory, Vol. 7, No. 4 (2013), pp. 981-999; arXiv preprint, arXiv:1108.5209 [math.NT], 2012.
R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, arXiv:0903.2514 [math.NT], 2009-2011; Eq. (106) page 17.
EXAMPLE
0.34537206410298648767349682789103371072066562538041...
MATHEMATICA
$MaxExtraPrecision = 200; m0 = 1000; dm = 200; digits = 105; Clear[f]; f[m_] := f[m] = (slog = Normal[Series[Log[1 - 1/((p - 1)^2*(p + 1))], {p, Infinity, m}]]; Exp[slog] /. Power[p, n_] -> PrimeZetaP[-n] // N[#, digits + 10] &); f[m = m0]; Print[m, " ", f[m]]; f[m = m + dm]; While[Print[m, " ", f[m]]; RealDigits[f[m], 10, digits + 5] != RealDigits[f[m - dm], 10, digits + 5], m = m + dm]; B = Exp[-EulerGamma]*f[m]; RealDigits[B, 10, digits] // First (* Jean-François Alcover, Sep 20 2015 *)
PROG
(PARI) exp(-Euler) * prodeulerrat(1-1/((p-1)^2*(p+1))) \\ Amiram Eldar, Mar 09 2021
CROSSREFS
Sequence in context: A343262 A298734 A137926 * A090395 A168485 A276737
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
More digits from Jean-François Alcover, Sep 20 2015
STATUS
approved

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 March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)