A394088 - OEIS

%I #5 Mar 10 2026 13:34:51

%S 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,

%T 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,

%U 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

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

%C 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.

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

%e 0.504218883262417684726585962603297309097398961445386...

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

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 10 2026