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.
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
KEYWORD
frac,nonn
AUTHOR
Leroy Quet, Aug 25 2004
EXTENSIONS
More terms from Emeric Deutsch and Max Alekseyev, Apr 13 2005
STATUS
approved