OFFSET
2,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1000
FORMULA
The rationals are r(m) = Zeta(2; m-1) - (m-1)/m^2, m >= 2, with the partial sums Zeta(2; n) = Sum_{k=1..n} 1/k^2. See the W. Lang link in A103345.
O.g.f. for the rationals r(m), m>=2: log(1-x) + polylog(2,x)/(1-x).
EXAMPLE
The rationals a(m)/A120077(m), m>=2, begin with (3/4, 37/36, 169/144, 4549/3600, 4769/3600, ...).
MATHEMATICA
Table[Numerator[HarmonicNumber[n, 2] -1/n], {n, 2, 40}] (* G. C. Greubel, Apr 24 2023 *)
PROG
(Magma)
A120076:= func< n | Numerator( (&+[1/k^2: k in [1..n]]) -1/n) >;
[A120076(n): n in [2..30]]; // G. C. Greubel, Apr 24 2023
(SageMath)
def A120076(n): return numerator(harmonic_number(n, 2) - 1/n)
[A120076(n) for n in range(2, 31)] # G. C. Greubel, Apr 24 2023
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Jul 20 2006
STATUS
approved