cp's OEIS Frontend

A349522 Decimal expansion of Sum_{k>=2} 1/(k*log(k))^2.

%I A349522 #30 Nov 23 2021 10:36:12
%S A349522 6,9,2,6,0,5,8,1,4,6,7,4,2,4,9,3,2,7,5,1,3,8,6,3,9,4,8,8,6,1,9,5,6,3,
%T A349522 0,5,4,3,5,9,2,1,7,3,3,4,9,5,1,7,2,4,9,4,3,7,5,3,9,9,0,7,6,3,3,7,2,3,
%U A349522 8,5,5,9,9,2,1,2,9,2,6,6,8,2,1,7,1
%N A349522 Decimal expansion of Sum_{k>=2} 1/(k*log(k))^2.
%C A349522 Theorem: Bertrand series Sum_{n>=2} 1/(n^q*log(n)^r) is convergent if q > 1.
%C A349522 Application for q = 2 with A201994 (r=-2), A073002 (r=-1), A013661 (r=0), A168218 (r=1), this sequence (r=2).
%H A349522 Wikipédia, <a href="https://fr.wikipedia.org/wiki/Série_de_Bertrand">Série de Bertrand</a> (in French).
%H A349522 Wikipedia, <a href="https://en.wikipedia.org/wiki/Joseph_Bertrand">Joseph Bertrand</a>.
%F A349522 Equals Sum_{k>=2} 1/(k*log(k))^2.
%F A349522 Equals Integral_{x>=2, y>=2} (zeta(x + y - 2) - 1) dx dy. - _Amiram Eldar_, Nov 21 2021
%e A349522 0.6926058...
%o A349522 (PARI) sumpos(k=2, 1/(k*log(k))^2) \\ _Michel Marcus_, Nov 21 2021
%Y A349522 Cf. A013661, A073002, A168218, A201994.
%K A349522 nonn,cons
%O A349522 0,1
%A A349522 _Bernard Schott_, Nov 20 2021