A278419 - OEIS

%I #16 Mar 08 2023 05:13:44

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

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

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

%N Decimal expansion of sum of cubes of reciprocals of nonprime numbers.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ZetaFunction.html">Zeta Function</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>.

%F Sum_{n>=1} 1/n^3 - Sum_{n>=1} 1/prime(n)^3.

%F Equals zeta(3) - primezetaP(3).

%F Sum of cubes of reciprocals of composite numbers = zeta(3) - primezetaP(3) - 1 = 0.02729426386...

%e 1.0272942638601507489766248468457432897895741704143495919035995386402...

%t RealDigits[Zeta[3] - PrimeZetaP[3], 10, 104][[1]]

%o (PARI) zeta(3) - sumeulerrat(1/p, 3) \\ _Amiram Eldar_, Mar 19 2021

%Y Cf. A275647.

%K nonn,cons

%O 1,3

%A _Jean-François Alcover_, Nov 21 2016