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

1,3

Links

Table of n, a(n) for n=1..104.

Eric Weisstein's World of Mathematics, Zeta Function.

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

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...

Example

1.0272942638601507489766248468457432897895741704143495919035995386402...

Mathematica

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

Prog

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

Crossrefs

Cf. A275647.

Sequence in context: A088666 A170854 A215140 * A197133 A178206 A245976

Adjacent sequences: A278416 A278417 A278418 * A278420 A278421 A278422

Keyword

nonn,cons

Author

Jean-François Alcover, Nov 21 2016

Status

approved