A335777 - OEIS

%I #17 Jun 26 2020 06:05:42

%S 1,3,9,0,2,0,7,5,4,3,4,4,3,7,4,6,8,5,4,2,3,3,5,6,5,7,8,4,4,9,8,5,3,1,

%T 6,8,5,8,8,8,3,9,6,9,8,3,9,2,3,6,0,3,6,3,6,3,9,2,5,0,8,2,6,2,0,8,5,2,

%U 9,3,3,5,0,5,3,5,3,4,9,5,7,4,4,2,1,6,4,0,8,3,9,2,0,3,0,7,1,1,3,9,6,3,0,7,8

%N Decimal expansion of Sum_{m>=1, k>=1} 1/(1 + m*k)^2.

%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/1356430/what-is-sum-sum-limits-m-n-geq1-frac11mn2">What is sum ?</a>, 2015.

%F Equals 1/4 + Sum_{j>=2} (j-1) * (-1)^j * (zeta(j)^2 - 1).

%F Equals Sum_{k>=1} d(k)/(k+1)^2, where d(k) is the number of divisors of k (A000005).

%e 1.39020754344374685423356578449853168588839698392360363639250826208529335...

%o (PARI) default(realprecision, 120); 1/4 + sumalt(j=2, (j-1)*(-1)^j*(zeta(j)^2 - 1))

%Y Cf. A013661, A259171.

%K nonn,cons

%O 1,2

%A _Vaclav Kotesovec_, Jun 26 2020