A323669 Decimal expansion of 15/(2*Pi^2) = 1/((4/5)*zeta(2)).

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

Offset: 0

Author

Wolfdieter Lang, Sep 03 2019

Keywords

• nonn
• cons
• easy

Comments

This is the limit n -> infinity of (1/n^2)*Phi_1(n) = (1/n^2)*Sum_{k=1..n} psi(k), with Dedekind's psi function psi(k) = k*Product_{p|k} (1 + 1/p) = A001615(k). Distinct primes p dividing k appear, and the empty product for k = 1 is set to 1. See the Walfisz reference, Satz 2., p. 100 (with x -> n, and phi_1(n) = psi(n)).

For the rationals r(n) = (1/n^2)*Phi_1(n) see A327340(n)/A327341(n), n >= 1.

Examples

			0.7599088773175332858290959740729572917826908100418491163420677392062984...
		

References

• Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, p. 100, Satz 2.

Links

• Eric Weisstein's World of Mathematics, Dedekind Function
• Wikipedia, Dedekind psi function
• Index entries for transcendental numbers

Crossrefs

Cf. A001615, A059956 (1/zeta(2)), A327340, A327341.

Programs

Mathematica

RealDigits[15/2/Pi^2, 10, 100][[1]] (* Amiram Eldar, Sep 03 2019 *)

PARI

15/(2*Pi^2) \\ Felix Fröhlich, Sep 04 2019

Formula

Equal to 15/(2*Pi^2) = 1/((4/5)*zeta(2)), with 1/zeta(2) = A059956.