A335005 - OEIS

%I #7 May 19 2020 19:16:18

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

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

%H 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 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 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 Equals zeta(2)/(2*zeta(3)) = A013661/(2*A002117) = A072691/A002117 = 1/(2*A253905).

%e 0.68421638881010293786838292699239597056540695732620...

%t RealDigits[Pi^2/12/Zeta[3], 10, 100][[1]]

%o (PARI) Pi^2/(12*zeta(3)) \\ _Michel Marcus_, May 19 2020

%Y Cf. A002117(zeta(3)), A013661 (zeta(2)), A034448, A064609, A072691 (Pi^2/12), A253905 (zeta(3)/zeta(2)).

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 19 2020