A335006 Decimal expansion of gamma - zeta'(2)/zeta(2), where gamma is the Euler-Mascheroni constant.

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

Offset: 1

Author

Amiram Eldar, May 19 2020

Keywords

• nonn
• cons

Examples

			1.1471766579960656670063764501021324334456416167468...
		

Links

• Eckford Cohen, Arithmetical Functions of a Greatest Common Divisor. I, Proceedings of the American Mathematical Society, Vol. 11, No. 2 (1960), pp. 164-171.

Crossrefs

Cf. A000010 (phi), A001620 (gamma), A013661 (zeta(2)), A073002 (-zeta'(2)).

Programs

Mathematica

RealDigits[EulerGamma - Zeta'[2]/Zeta[2], 10, 100][[1]]

PARI

Euler - zeta'(2)/zeta(2) \\ Michel Marcus, May 19 2020

Formula

Equals lim_{k->oo} zeta(2) * Sum_{i=1..k} phi(i)/i^2 - log(k), where phi is the Euler totient function (A000010).

Equals A001620 + A073002/A013661.