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A124175 Decimal expansion of Product_{primes p} ((p-1)/p)^(1/p)). 12
5, 5, 9, 8, 6, 5, 6, 1, 6, 9, 3, 2, 3, 7, 3, 4, 8, 5, 7, 2, 3, 7, 6, 2, 2, 4, 4, 2, 2, 3, 4, 1, 6, 7, 1, 7, 2, 5, 7, 6, 6, 6, 3, 7, 0, 2, 1, 2, 9, 0, 6, 0, 3, 9, 5, 5, 4, 2, 3, 3, 9, 3, 3, 9, 3, 5, 2, 0, 3, 1, 7, 1, 7, 9, 7, 5, 9, 1, 5, 9, 3, 6, 2, 7, 6, 5, 4, 0, 9, 5, 0, 6, 3, 0, 6, 6, 5, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This might be interpreted as the expected value of phi(n)/n for very large n.

LINKS

Table of n, a(n) for n=0..98.

Mathoverflow, Asymptotics of product of Euler's totient function, 2016.

Eric Weisstein's World of Mathematics, Prime Zeta Function

FORMULA

exp(-suminf(h=1, primezeta(h+1)/h)). - Robert Gerbicz

{Notation not clear. Is this perhaps exp(-Sum_{h=1..oo} primezeta(h+1)/h) ? - N. J. A. Sloane, Oct 08 2017)

Equals lim_{n->infinity} (A001088(n)/n!)^(1/n). - Vaclav Kotesovec, Feb 05 2016

EXAMPLE

0.5598656169323734857237622442234167172576663702129060395542339339\

352031717975915936276540950630665470795373094197373037280781542375...

MATHEMATICA

digits = 100; s = Exp[-NSum[PrimeZetaP[h+1]/h, {h, 1, Infinity}, WorkingPrecision -> digits+5, NSumTerms -> 3 digits]]; RealDigits[s, 10, digits][[1]] (* Jean-François Alcover, Dec 07 2015, after Robert Gerbicz *)

PROG

(PARI) default(realprecision, 256); (f(k)=return(sum(n=1, 512, moebius(n)/n*log(zeta(k*n))))); exp(sum(h=1, 512, -1/h*f(h+1))) /* Robert Gerbicz */

(PARI) exp(-suminf(m=2, log(zeta(m))*sumdiv(m, k, if(k<m, moebius(k)/(m-k), 0)))) /* Martin Fuller */

CROSSREFS

Cf. A126226, A085548, A085541, A085964 - A085969, A242624, A272028.

Sequence in context: A021951 A206772 A200679 * A168277 A163980 A333154

Adjacent sequences:  A124172 A124173 A124174 * A124176 A124177 A124178

KEYWORD

nonn,cons

AUTHOR

David W. Wilson, Dec 05 2006

EXTENSIONS

Robert Gerbicz computed this to 130 decimal places.

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)