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A218342 Decimal expansion of e^-gamma * prod (1 - 1/(p^3 - p^2 - p + 1)) where the product is over all primes p. 1
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

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

Paul Erdős, Carl Pomerance, and Eric Schmutz, Carmichael's lambda function, Acta Arithmetica 58 (1991), pp. 363-385.

Sungjin Kim, An Average Result on the Order of 'a' modulo 'n', arXiv:1509.03768 [math.NT], 2015.

Pär Kurlberg and Carl Pomerance, On a problem of Arnold: the average multiplicative order of a given integer, 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], Eq. (106) page 17.

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 *)

CROSSREFS

Cf. A002322, A036391.

Sequence in context: A178231 A298734 A137926 * A090395 A168485 A276737

Adjacent sequences:  A218339 A218340 A218341 * A218343 A218344 A218345

KEYWORD

nonn,cons

AUTHOR

Charles R Greathouse IV, Oct 26 2012

EXTENSIONS

More digits from Jean-François Alcover, Sep 20 2015

STATUS

approved

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Last modified October 22 09:31 EDT 2019. Contains 328315 sequences. (Running on oeis4.)