cp's OEIS Frontend

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

%I A152441 #19 Mar 31 2025 08:05:02
%S A152441 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,
%T A152441 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,
%U A152441 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
%N A152441 Decimal expansion of Sum_{primes p} 1/(p^2*(p-1)).
%C A152441 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).
%H A152441 <a href="/wiki/Index_to_constants#Start_of_section_P">Index to constants which are prime zeta sums</a> {2,1,0}
%F A152441 Equals A136141 minus A085548 .
%F A152441 Equals Sum_{n>=1} 1/A246549(n). - _Amiram Eldar_, Oct 27 2020
%e A152441 0.320909249008729629357824095023694461445509992843293626574587137005544001125... = 1/(4*1) + 1/(9*2) + 1/(25*4) + 1/(49*6) + ...
%t A152441 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 *)
%o A152441 (PARI) sumeulerrat(1/(p^2*(p-1))) \\ _Amiram Eldar_, Mar 18 2021
%Y A152441 Cf. A085548, A136141, A246549.
%K A152441 cons,nonn
%O A152441 0,1
%A A152441 _R. J. Mathar_, Dec 04 2008
%E A152441 More digits from _Jean-François Alcover_, Sep 11 2015