A334313 - OEIS

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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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..32.

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.

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}]]

PROG

(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