A334314 Numerators of the partial sums of the Möbius transform of the harmonic numbers.

1, 3, 7, 35, 21, 259, 1241, 5497, 475, 19367, 7473, 54193, 307727, 485041, 1109501, 9353753, 7870991, 189509941, 1048445929, 4213673063, 96924859, 68325181, 3156755829, 113847868229, 3353128913, 614935296797, 120633624344, 1937548941997, 70096529185, 62887637910847

Offset: 1

Author

Mats Granvik, Apr 22 2020

Keywords

• nonn
• frac

Crossrefs

Denominators are in A334313.

Cf. A001008 (numerators of harmonic numbers), A334312.

Programs

Mathematica

nn = 30; Numerator[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) = numerator(sum(m=1, n, sumdiv(m, d, moebius(m/d)*sum(i=1, d, 1/i)))); \\ Michel Marcus, Apr 23 2020

Formula

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

a(n)/A334313(n) = Sum_{k=1..n} A334312(n,k)/k.