A396587 a(n) / (4*n!) is the cubic moment of the Farey series of order n.

4, 9, 35, 182, 1294, 9444, 92028, 892464, 10128816, 117254880, 1652683680, 21828044160, 352740804480, 5498803134720, 93640868294400, 1664328537446400, 33649819347916800, 644822365353062400, 14325994022364057600, 306469676914329600000, 7078149345359554560000

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Formula

a(n) = 4 * n! * Sum_{r in F_n} r^3 where F_n is the Farey series of order n.

a(n) / (4*n!) = 1/2 + (1/4) * Sum_{m=1..n} (phi(m)+J(m,-1)) where phi is the Euler totient and J is the Jordan totient.

Crossrefs

Cf. A006842, A006843, A396586.

Sequence in context: A182723 A176607 A134815 * A367992 A352002 A120073

Adjacent sequences: A396584 A396585 A396586 * A396588 A396589 A396590

Keyword

nonn

Author

Marko Riedel, May 29 2026

Status

approved