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A336284 Decimal expansion of Sum_{n>=2} n^(log(n))/log(n)^n.

%I A336284 #29 Dec 21 2024 13:18:11
%S A336284 1,0,5,4,1,7,0,5,1,1,5,2,2,8,9,7,1,5,9,1,2,6,9,7,1,5,3,3,6,0,6,3,0,9,
%T A336284 2,9,4,7,4,7,1,7,4,8,9,9,6,5,8,8,3,0,6,5,0,3,6,9,4,9,0,6,6,6,9,0,8,6,
%U A336284 3,4,7,2,6,3,5,4,3,0,5,7,7,0,2,9,3,5,9,9,7
%N A336284 Decimal expansion of Sum_{n>=2} n^(log(n))/log(n)^n.
%C A336284 This series is convergent because there exists n_1 such that for n >= n_1, n^(log(n))/log(n)^n <= (1/sqrt(e))^n.
%F A336284 Equals Sum_{n>=2} n^(log(n))/log(n)^n.
%e A336284 10.5417051152289715912697153360630929474717489965883...
%p A336284 evalf(sum(n^(log(n))/log(n)^n, n=2..infinity),100);
%o A336284 (PARI) suminf(n=2, n^(log(n))/log(n)^n) \\ _Michel Marcus_, Jul 17 2020
%Y A336284 Cf. A073009 (1/n^n), A099870 (1/n^log(n)), A099871 (1/log(n)^n), A308915 (1/(log(n)^log(n))).
%Y A336284 Cf. A092605 (1/sqrt(e)).
%K A336284 nonn,cons
%O A336284 2,3
%A A336284 _Bernard Schott_, Jul 17 2020