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A065484 Decimal expansion of product(1 + p/((p-1)^2*(p+1))), p prime >= 2). 5
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Decimal expansion of totient constant. - Eric W. Weisstein, Apr 20 2006

LINKS

Table of n, a(n) for n=1..99.

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

Eric Weisstein's World of Mathematics, Totient Summatory Function

FORMULA

Equals Pi^2 * A065483 / 6.

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

EXAMPLE

2.203856596437859787872828316480...

MATHEMATICA

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

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 *)

CROSSREFS

Cf. A077387, A065483.

Sequence in context: A218033 A255903 A118262 * A255970 A011137 A143396

Adjacent sequences:  A065481 A065482 A065483 * A065485 A065486 A065487

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane, Nov 19 2001, Aug 09 2010

STATUS

approved

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Last modified August 22 20:47 EDT 2019. Contains 326209 sequences. (Running on oeis4.)