A152441 Decimal expansion of Sum_{primes p} 1/(p^2*(p-1)).

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

Offset: 0

Author

R. J. Mathar, Dec 04 2008

Keywords

• cons
• nonn

Comments

Generally, sum_p 1/(p^s*(p-1)) equals A136141 minus the sum over all prime zeta functions with index 2 to s (see A085964 to A085969).

Examples

			0.320909249008729629357824095023694461445509992843293626574587137005544001125... = 1/(4*1) + 1/(9*2) + 1/(25*4) + 1/(49*6) + ...
		

Links

• Index to constants which are prime zeta sums {2,1,0}

Crossrefs

Cf. A085548, A136141, A246549.

Programs

Mathematica

digits = 104; sp = NSum[PrimeZetaP[n], {n, 3, Infinity},  WorkingPrecision -> digits + 10, NSumTerms -> 2*digits]; RealDigits[sp, 10, digits] // First (* Jean-François Alcover, Sep 11 2015 *)

PARI

sumeulerrat(1/(p^2*(p-1))) \\ Amiram Eldar, Mar 18 2021

Formula

Equals A136141 minus A085548 .

Equals Sum_{n>=1} 1/A246549(n). - Amiram Eldar, Oct 27 2020

Extensions

More digits from Jean-François Alcover, Sep 11 2015