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

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

Offset: 0

Author

Amiram Eldar, May 19 2020

Keywords

• nonn
• cons

Examples

			0.68421638881010293786838292699239597056540695732620...
		

Links

• Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Mathematische Zeitschrift, Vol. 74, No. 1 (1960), pp. 66-80.
• R. Sitaramachandrarao and D. Suryanarayana, On Sigma_{n<=x} sigma*(n) and Sigma_{n<=x} phi*(n), Proceedings of the American Mathematical Society, Vol. 41, No. 1 (1973), pp. 61-66.

Crossrefs

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

Programs

Mathematica

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

PARI

Pi^2/(12*zeta(3)) \\ Michel Marcus, May 19 2020

Formula

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.

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