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A065484 Decimal expansion of product(1 + p/((p-1)^2*(p+1))), p prime >= 2). 5

%I

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

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

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

%N Decimal expansion of product(1 + p/((p-1)^2*(p+1))), p prime >= 2).

%C Decimal expansion of totient constant. - _Eric W. Weisstein_, Apr 20 2006

%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a> [Cached copy]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientSummatoryFunction.html">Totient Summatory Function</a>

%F Equals Pi^2 * A065483 / 6.

%F Also defined as: Sum_{m>=1} 1/(m*A000010(m)). See Weisstein link.

%e 2.203856596437859787872828316480...

%t $MaxExtraPrecision = 500; digits = 99; terms = 500; P[n_] := PrimeZetaP[n];

%t LR = Join[{0, 0, 0}, LinearRecurrence[{2, -1, -1, 1}, {3, 4, 5, 3}, terms + 10]]; r[n_Integer] := LR[[n]]; (Pi^2/6)*Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10] ] // RealDigits[#, 10, digits]& // First (* _Jean-Fran├žois Alcover_, Apr 18 2016 *)

%Y Cf. A077387, A065483.

%K cons,nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 19 2001, Aug 09 2010

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Last modified September 22 05:47 EDT 2019. Contains 327287 sequences. (Running on oeis4.)