A397531 Decimal expansion of Sum_{k>=1} H(k,4)/k^2, where H(k,4) = A007410(k)/A007480(k) is the k-th generalized harmonic number of order 4.

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2nd ed., 2023, section 4.2.11, p. 293, eq. (4.57).

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.21, p. 292, section 5.21, p. 319, section 6.21, pp. 384-392, eq. (6.72).

Index entries for sequences related to harmonic numbers.

Formula

Equals 37*zeta(6)/12 - zeta(3)^2.

Example

1.691866976018417280206078538048350467180201855170743...

Mathematica

RealDigits[37*Zeta[6]/12 - Zeta[3]^2, 10, 120][[1]]

Prog

(PARI) 37*zeta(6)/12 - zeta(3)^2

Crossrefs

Cf. A007410, A007480.

Cf. A002117, A013664.

Sequence in context: A357066 A179593 A117871 * A011454 A379105 A274480

Adjacent sequences: A397528 A397529 A397530 * A397532 A397533 A397534

Keyword

nonn,cons,new

Author

Amiram Eldar, Jun 30 2026

Status

approved