A334313 Denominators of the partial sums of the Möbius transform of the harmonic numbers.

1, 2, 3, 12, 5, 60, 210, 840, 63, 2520, 770, 5544, 25740, 40040, 90090, 720720, 510510, 12252240, 58198140, 232792560, 5290740, 3695120, 148728580, 5354228880, 147094200, 26771144400, 5019589575, 80313433200, 2587877292, 2329089562800, 36100888223400, 3702655202400

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = denominator of Sum_{m=1..n} Sum_{d|m} H(d)*mu(m/d).

A334314(n)/a(n) = Sum_{k=1..n} A334312(n,k)/k.

Mathematica

nn = 32; Denominator[Table[Sum[Sum[If[Mod[n, k] == 0, MoebiusMu[n/k]*HarmonicNumber[k], 0], {k, 1, n}], {n, 1, m}], {m, 1, nn}]]

Prog

(PARI) a(n) = denominator(sum(m=1, n, sumdiv(m, d, moebius(m/d)*sum(i=1, d, 1/i)))); \\ Michel Marcus, Apr 23 2020

Crossrefs

Numerators are in A334314.

Cf. A334312.

Sequence in context: A245678 A124444 A038610 * A325760 A056819 A124442

Adjacent sequences: A334310 A334311 A334312 * A334314 A334315 A334316

Keyword

nonn,frac

Author

Mats Granvik, Apr 23 2020

Status

approved