A065487 Decimal expansion of Product_{p prime} (1 + 1/(p*(p^2-1))).

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

Offset: 1

Author

N. J. A. Sloane, Nov 19 2001

Keywords

• cons
• nonn

Examples

			1.2312911488886035627747876512720337...
		

Links

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

Crossrefs

Cf. A000010, A001615, A003557, A036966, A047994, A072802.

Programs

Mathematica

$MaxExtraPrecision = 600; digits = 99; terms = 600; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0}, LinearRecurrence[{0, 2, -1, -1, 1}, {3, 0, 5, -3, 7}, 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*(p^2-1))) \\ Amiram Eldar, Mar 17 2021

Formula

Equals Sum_{k>=1} 1/A001615(A036966(k)). - Amiram Eldar, Jun 23 2020

Equals Sum_{k>=1} A003557(k)/k^3. - Amiram Eldar, Jan 25 2024

Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A047994(k)/A000010(k). - Amiram Eldar, Feb 04 2024