A397451 - OEIS

A397451

Decimal expansion of Sum_{k>=1} sigma(k) * log(k) / k^4, where sigma(k) is the sum of divisors of k (A000203).

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

FORMULA

Equals zeta(4) * (-zeta'(3) - zeta(3) * (gamma + log(2*Pi) + 120*log(A_3))), where gamma is Euler's constant (A001620), and A_3 = A243263.

EXAMPLE

0.297271898758924704455828564992645553857265656949487...

MATHEMATICA

RealDigits[Zeta[4] * (-Zeta'[3] - Zeta[3]*(EulerGamma + Log[2*Pi] - 120*Zeta'[-3] - 11/6)), 10, 120][[1]]

PROG

(PARI) zeta(4) * (-zeta'(3) - zeta(3)*(Euler + log(2*Pi) - 120*zeta'(-3) - 11/6))

CROSSREFS

Cf. A000203, A001620, A073002, A074962, A183700 (Sum_{k>=1} sigma(k)/k^4), A243263, A398011.

Sequence in context: A230480 A393777 A335605 * A308320 A254140 A200991

Adjacent sequences: A397448 A397449 A397450 * A397452 A397453 A397454

KEYWORD

nonn,cons,new

AUTHOR

Amiram Eldar, Aug 21 2026

STATUS

approved