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A065483 Decimal expansion of totient constant Product_{p prime} (1 + 1/(p^2*(p-1))). 13
1, 3, 3, 9, 7, 8, 4, 1, 5, 3, 5, 7, 4, 3, 4, 7, 2, 4, 6, 5, 9, 9, 1, 5, 2, 5, 8, 6, 5, 1, 4, 8, 8, 6, 0, 5, 2, 7, 7, 5, 2, 4, 2, 2, 4, 9, 7, 8, 8, 1, 8, 2, 8, 0, 6, 6, 6, 3, 0, 1, 5, 0, 6, 7, 6, 4, 6, 7, 9, 4, 8, 2, 7, 2, 7, 6, 0, 0, 9, 8, 2, 3, 7, 3, 7, 3, 4, 3, 6, 6, 4, 4, 0, 8, 5, 0, 4, 5, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The sum of the reciprocals of the cubefull numbers (A036966). - Amiram Eldar, Jun 23 2020
LINKS
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 86.
Eric Weisstein's World of Mathematics, Totient Summatory Function
FORMULA
Equals (6/Pi^2) * A065484. - Amiram Eldar, Jun 23 2020
EXAMPLE
1.339784153574347246599152586514886052775...
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]]; Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 18 2016 *)
PROG
(PARI) prodeulerrat(1 + 1/(p^2*(p-1))) \\ Vaclav Kotesovec, Sep 19 2020
CROSSREFS
Sequence in context: A156164 A198613 A197031 * A019745 A173815 A188615
KEYWORD
cons,nonn
AUTHOR
N. J. A. Sloane, Nov 19 2001
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)