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
Examples
Sum_{k>=2} 1/(k^3*log(k)) = 0.23799610019862130199...
Programs
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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
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PARI
intnum(x=3, [oo, log(3)], zeta(x)-1) \\ following Charles R Greathouse IV's program for A168218
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PARI
sumpos(k=2, 1/(k^3*log(k))) \\ Michel Marcus, Nov 27 2021
Formula
Equals Integral_{s=3..oo} (zeta(s) - 1) ds.