A335007 Decimal expansion of 2*(gamma - zeta'(2)/zeta(2)) - 1, where gamma is the Euler-Mascheroni constant.

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

Offset: 1

Author

Amiram Eldar, May 19 2020

Keywords

• nonn
• cons

Examples

			1.2943533159921313340127529002042648668912832334937...
		

Links

• Eckford Cohen, The number of unitary divisors of an integer, The American Mathematical Monthly, Vol. 67, No. 9 (1960), pp. 879-880.

Crossrefs

Cf. A001620 (gamma), A013661 (zeta(2)), A034444, A064608, A073002 (-zeta'(2)), A147533, A335006.

Programs

Mathematica

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

PARI

2*Euler - 2*zeta'(2)/zeta(2) - 1 \\ Michel Marcus, May 19 2020

Formula

Equals lim_{k->oo} ((zeta(2)/k)*A064608(k) - log(k)) where A064608 is the partial sums of the number of unitary divisors (A034444).

Equals 2*A001620 + 2*A073002/A013661 - 1 = 2*A335006 - 1.