A349641 Decimal expansion of the Sum_{k>=2} 1/(k^3*log(k)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..98.

Formula

Equals Integral_{s=3..oo} (zeta(s) - 1) ds.

Example

Sum_{k>=2} 1/(k^3*log(k)) = 0.23799610019862130199...

Mathematica

(* following Jean-François Alcover's Mathematica program for A168218 *) digits = 110; NSum[ 1/(n^3*Log[n]), {n, 2, Infinity}, NSumTerms -> 500000, WorkingPrecision -> digits + 5, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 12}}] // RealDigits[#, 10, digits] & // First

Prog

(PARI) intnum(x=3, [oo, log(3)], zeta(x)-1) \\ following Charles R Greathouse IV's program for A168218
(PARI) sumpos(k=2, 1/(k^3*log(k))) \\ Michel Marcus, Nov 27 2021

Crossrefs

Similar sequences: A013661, A002117, A073002, A244115, A168218.

Sequence in context: A378827 A168222 A323384 * A140221 A046668 A047533

Adjacent sequences: A349638 A349639 A349640 * A349642 A349643 A349644

Keyword

nonn,cons

Author

Jianing Song, Nov 24 2021

Status

approved