A286229 Decimal expansion of Sum_{p prime} 1/(p^3 - 1).

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

Offset

0,2

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Prime Zeta Function.

Eric Weisstein's World of Mathematics, Prime Sums.

Formula

Equals Sum_{k>=1} primezeta(3*k).

More generally, Sum_{p prime} 1/(p^s - 1) = Sum_{k>=1} primezeta(s*k).

Example

1/(2^3 - 1) + 1/(3^3 - 1) + 1/(5^3 - 1) + ... = 1/2^3 + 1/3^3 + 1/5^3 + ... + 1/2^6 + 1/3^6 + 1/5^6 + ... + 1/2^9 + 1/3^9 + 1/5^9 + ... = 0.19411816983263379229...

Mathematica

digits = 105; sp = NSum[PrimeZetaP[3 n], {n, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 2*digits]; RealDigits[sp, 10, digits] // First

Prog

(PARI) sumeulerrat(1/(p^3-1)) \\ Amiram Eldar, Mar 18 2021

Crossrefs

Cf. A030078, A085541, A154945.

Sequence in context: A270309 A010158 A336274 * A242611 A098454 A298531

Adjacent sequences: A286226 A286227 A286228 * A286230 A286231 A286232

Keyword

nonn,cons

Author

Ilya Gutkovskiy, May 04 2017

Status

approved