A247667 Decimal expansion of the coefficient c_m in c_m*log(N), the asymptotic mean number of factors in a random factorization of n <= N.

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

Offset: 0

Author

Jean-François Alcover, Sep 22 2014

Keywords

• nonn
• cons

Examples

			0.55001000541315449183305812670222219646116822710271404...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 41.

Crossrefs

Cf. A107311, A129373, A129374, A129375, A217598, A247668.

Programs

Mathematica

digits = 101; rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> digits+5]; cm = -1/Zeta'[rho]; RealDigits[cm, 10, digits] // First

Formula

c_m = -1/zeta'(rho), where rho = 1.728647... is A107311, the real solution to zeta(rho) = 2.

Residue_{s = rho} 1/(2 - Zeta(s)). - Vaclav Kotesovec, Nov 04 2018