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A334314 Numerators of the partial sums of the Möbius transform of the harmonic numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

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.

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}]]

PROG

(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

CROSSREFS

Denominators are in A334313.

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

Sequence in context: A081890 A192880 A318444 * A179115 A299300 A047907

Adjacent sequences:  A334311 A334312 A334313 * A334315 A334316 A334317

KEYWORD

nonn,frac

AUTHOR

Mats Granvik, Apr 22 2020

STATUS

approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)