A394087 Decimal expansion of Sum_{k>=1} k * (1/zeta(2*k+2)-1/zeta(2*k)).

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

Offset

0,1

Comments

The asymptotic mean of the maximum exponent in the prime factorization of the greatest common divisor of two positive integers selected independently at random.

Links

Table of n, a(n) for n=0..105.

Formula

Equals lim_{m->oo} (1/m^2) * Sum_{i,j=1..m} A051903(gcd(i, j)).

Example

0.490563930351797385989313206771367532375639509515802...

Prog

(PARI) sumpos(k = 1, k*(1/zeta(2*k+2)-1/zeta(2*k)))

Crossrefs

Cf. A033150, A051903, A393778, A394088.

Sequence in context: A021208 A298813 A021675 * A093872 A097906 A373204

Adjacent sequences: A394084 A394085 A394086 * A394088 A394089 A394090

Keyword

nonn,cons

Author

Amiram Eldar, Mar 10 2026

Status

approved