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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
OFFSET
1,2
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: A355156 A365140 A318444 * A179115 A299300 A047907
KEYWORD
nonn,frac
AUTHOR
Mats Granvik, Apr 22 2020
STATUS
approved