A278419 Decimal expansion of sum of cubes of reciprocals of nonprime numbers.

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, 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, 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

Offset: 1

Author

Jean-François Alcover, Nov 21 2016

Keywords

• nonn
• cons

Examples

			1.0272942638601507489766248468457432897895741704143495919035995386402...
		

Links

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

Crossrefs

Cf. A275647.

Programs

Mathematica

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

PARI

zeta(3) - sumeulerrat(1/p, 3) \\ Amiram Eldar, Mar 19 2021

Formula

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

Equals zeta(3) - primezetaP(3).

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