A065483 Decimal expansion of totient constant Product_{p prime} (1 + 1/(p^2*(p-1))).

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

Offset: 1

Author

N. J. A. Sloane, Nov 19 2001

Keywords

• cons
• nonn

Comments

The sum of the reciprocals of the cubefull numbers (A036966). - Amiram Eldar, Jun 23 2020

Examples

			1.339784153574347246599152586514886052775...
		

Links

• Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 86.
• G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
• Eric Weisstein's World of Mathematics, Totient Summatory Function

Crossrefs

Cf. A036966, A065484, A078074.

Programs

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 *)

PARI

prodeulerrat(1 + 1/(p^2*(p-1))) \\ Vaclav Kotesovec, Sep 19 2020

Formula

Equals (6/Pi^2) * A065484. - Amiram Eldar, Jun 23 2020