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A097504 Denominator of b(n), where Sum_{k>=1} b(k)/k^r = 1/(Sum_{k>=1} H(k)/k^r). H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number. 1
1, 2, 6, 6, 60, 20, 140, 70, 280, 2520, 27720, 6930, 360360, 360360, 360360, 30030, 12252240, 1361360, 77597520, 29099070, 25865840, 11085360, 118982864, 446185740, 267711444, 1274816400, 2974571600, 10039179150, 2329089562800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For r = integer >= 2, Sum_{k>=1} b(k)/k^r also equals 1/(zeta(r+1)(r/2 + 1) - (1/2)Sum_{j=2..r-1} zeta(j)zeta(r+1-j)), where zeta(n) is Sum_{k>=1} 1/k^n.

LINKS

Table of n, a(n) for n=1..29.

FORMULA

b(1)=1; for n>=2, b(n) = -Sum_{k|n, k>=2} (H(k) b(n/k)).

EXAMPLE

1, -3/2, -11/6, 1/6, -137/60, 61/20, -363/140, ...

MAPLE

with(numtheory): H:=n->sum(1/j, j=1..n):b[1]:=1: for n from 2 to 32 do div:=sort(convert(divisors(n), list)):b[n]:=-sum(H(div[i])*b[n/div[i]], i=2..nops(div)) od: seq(denom(b[n]), n=1..32); # Emeric Deutsch

CROSSREFS

Cf. A096663.

Sequence in context: A228955 A328584 A226707 * A189144 A130726 A279841

Adjacent sequences:  A097501 A097502 A097503 * A097505 A097506 A097507

KEYWORD

frac,nonn

AUTHOR

Leroy Quet, Aug 25 2004

EXTENSIONS

More terms from Emeric Deutsch and Max Alekseyev, Apr 13 2005

STATUS

approved

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Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)