A349641 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; constant; graph; refs; listen; history; text; internal format)

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