A394088 Decimal expansion of 1/zeta(2)^2 + Sum_{k>=2} k * ((1/zeta(k)-1/zeta(k+1))^2).

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

Offset

0,1

Comments

The asymptotic mean of the common maximum exponent in the prime factorizations of two positive integers selected independently at random, defined as 0 if their maximum exponents differ.

The asymptotic mean over the pairs with a common maximum exponent is this constant divided by A393778, i.e., 1.17180286212502644048... .

Links

Table of n, a(n) for n=0..104.

Example

0.504218883262417684726585962603297309097398961445386...

Prog

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

Crossrefs

Cf. A033150, A051903, A013661, A227929, A393778, A394087.

Sequence in context: A099220 A229174 A021956 * A139341 A159575 A092173

Adjacent sequences: A394085 A394086 A394087 * A394089 A394090 A394091

Keyword

nonn,cons

Author

Amiram Eldar, Mar 10 2026

Status

approved