A088245 - OEIS

%I #35 Feb 16 2025 08:32:51

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

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

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

%N Decimal expansion of 9/(2*Pi^2).

%C The asymptotic density of squarefree numbers not divisible by 3 (A261034). - _Amiram Eldar_, May 22 2020

%D See the Hardy reference given under A030059, eq. (4.9.4), p. 64, from the corrected formula on p. 65 for s=2. - _Wolfdieter Lang_, Oct 18 2016

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoebiusFunction.html">Moebius Function</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Sum_{n > 0} 1/A030059(n)^2 (the sum of reciprocals of squarefree numbers with an odd number of prime factors). Convergence is very slow. - _Michel Lagneau_, Oct 23 2015

%e 0.455945326390519971497457584443774375...

%t RealDigits[N[9/(2 Pi^2), 120]] // First (* _Michael De Vlieger_, Oct 23 2015 *)

%o (PARI) 9/(2*Pi^2) \\ _Altug Alkan_, Oct 23 2015

%Y Cf. A082020, A088246, A030059, A261034.

%K nonn,cons,changed

%O 0,1

%A _Eric W. Weisstein_, Sep 25 2003