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, 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

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 * A356521 A189144 A367676

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