A335777 Decimal expansion of Sum_{m>=1, k>=1} 1/(1 + m*k)^2.

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Mathematics Stack Exchange, What is sum ?, 2015.

Formula

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

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

Example

1.39020754344374685423356578449853168588839698392360363639250826208529335...

Prog

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

Crossrefs

Cf. A013661, A259171.

Sequence in context: A272535 A016626 A126321 * A358945 A248726 A267411

Adjacent sequences: A335774 A335775 A335776 * A335778 A335779 A335780

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 26 2020

Status

approved