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A334313
Denominators of the partial sums of the Möbius transform of the harmonic numbers.
2
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
OFFSET
1,2
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
CROSSREFS
Numerators are in A334314.
Cf. A334312.
Sequence in context: A245678 A124444 A038610 * A325760 A056819 A124442
KEYWORD
nonn,frac
AUTHOR
Mats Granvik, Apr 23 2020
STATUS
approved