A067710 a(n) = n! * Sum_{k|n} (Sum_{j=1..k} 1/j); the k-sum is over the positive divisors, k, of n.

1, 5, 17, 110, 394, 4884, 18108, 294384, 2054736, 27986400, 160460640, 5733590400, 26029779840, 727452230400, 11030096851200, 223495556659200, 1579093018675200, 83918534992588800, 553210247226470400, 32584767906539520000, 463473994611898368000, 10352822932220719104000

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

E.g.f.: Sum_{k>0} log(1-x^k)/(x^k-1). - Vladeta Jovovic, Aug 01 2004

Example

a(6) = 6! *(1 + (1 + 1/2) + (1 + 1/2 + 1/3) + (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6)) because 1, 2, 3 and 6 are the divisors of 6.

Mathematica

a[n_] := n! * DivisorSum[n, HarmonicNumber[#] &]; Array[a, 20] (* Amiram Eldar, Aug 18 2023 *)

Prog

(PARI) a(n) = n!*sumdiv(n, k, sum(j=1, k, 1/j)); \\ Michel Marcus, Aug 20 2023

Crossrefs

Cf. A001008, A002805.

Sequence in context: A234797 A062586 A301641 * A197912 A203114 A198027

Adjacent sequences: A067707 A067708 A067709 * A067711 A067712 A067713

Keyword

nonn

Author

Leroy Quet, Feb 05 2002

Extensions

a(20)-a(22) from Amiram Eldar, Aug 18 2023

Status

approved