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Numerators of the partial sums of the Möbius transform of the harmonic numbers.
2

%I #17 May 06 2020 02:45:44

%S 1,3,7,35,21,259,1241,5497,475,19367,7473,54193,307727,485041,1109501,

%T 9353753,7870991,189509941,1048445929,4213673063,96924859,68325181,

%U 3156755829,113847868229,3353128913,614935296797,120633624344,1937548941997,70096529185,62887637910847

%N Numerators of the partial sums of the Möbius transform of the harmonic numbers.

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

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

%t 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}]]

%o (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

%Y Denominators are in A334313.

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

%K nonn,frac

%O 1,2

%A _Mats Granvik_, Apr 22 2020