cp's OEIS Frontend

A335005 Decimal expansion of Pi^2/(12*zeta(3)).

%I A335005 #7 May 19 2020 19:16:18
%S A335005 6,8,4,2,1,6,3,8,8,8,1,0,1,0,2,9,3,7,8,6,8,3,8,2,9,2,6,9,9,2,3,9,5,9,
%T A335005 7,0,5,6,5,4,0,6,9,5,7,3,2,6,2,0,6,9,6,1,0,3,8,6,7,6,5,9,6,3,8,4,1,7,
%U A335005 2,4,8,9,8,9,3,8,0,0,9,7,1,1,4,1,1,0,1
%N A335005 Decimal expansion of Pi^2/(12*zeta(3)).
%H A335005 Eckford Cohen, <a href="https://doi.org/10.1007/BF01180473">Arithmetical functions associated with the unitary divisors of an integer</a>, Mathematische Zeitschrift, Vol. 74, No. 1 (1960), pp. 66-80.
%H A335005 R. Sitaramachandrarao and D. Suryanarayana, <a href="https://doi.org/10.1090/S0002-9939-1973-0319922-9">On Sigma_{n<=x} sigma*(n) and Sigma_{n<=x} phi*(n)</a>, Proceedings of the American Mathematical Society, Vol. 41, No. 1 (1973), pp. 61-66.
%F A335005 Equals lim_{k->oo} A064609(k)/k^2, where A064609(k) is the partial sums of A034448, the sum of unitary divisors from 1 to k.
%F A335005 Equals zeta(2)/(2*zeta(3)) = A013661/(2*A002117) = A072691/A002117 = 1/(2*A253905).
%e A335005 0.68421638881010293786838292699239597056540695732620...
%t A335005 RealDigits[Pi^2/12/Zeta[3], 10, 100][[1]]
%o A335005 (PARI) Pi^2/(12*zeta(3)) \\ _Michel Marcus_, May 19 2020
%Y A335005 Cf. A002117(zeta(3)), A013661 (zeta(2)), A034448, A064609, A072691 (Pi^2/12), A253905 (zeta(3)/zeta(2)).
%K A335005 nonn,cons
%O A335005 0,1
%A A335005 _Amiram Eldar_, May 19 2020