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

Author

Mats Granvik, Apr 23 2020

Keywords

• nonn
• frac

Crossrefs

Numerators are in A334314.

Cf. A334312.

Programs

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}]]

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

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.