A053821 A discrete approximation to log(n): Sum_{ d divides n } A029833(d).

0, 1, 1, 1, 2, 2, 2, 1, 1, 3, 2, 2, 3, 3, 3, 1, 3, 2, 3, 3, 3, 3, 3, 2, 2, 4, 1, 3, 3, 4, 3, 1, 3, 4, 4, 2, 4, 4, 4, 3, 4, 4, 4, 3, 3, 4, 4, 2, 2, 3, 4, 4, 4, 2, 4, 3, 4, 4, 4, 4, 4, 4, 3, 1, 5, 4, 4, 4, 4, 5, 4, 2, 4, 5, 3, 4, 4, 5, 4, 3, 1, 5, 4, 4, 5, 5, 4, 3, 4, 4, 5, 4, 4

Offset: 1

Author

N. J. A. Sloane, Apr 08 2000

Keywords

• nonn
• easy

Comments

For n >= 1, log(n) = Sum_{ d divides n } Lambda(d), where Lambda is the real Mangoldt function (see A029833).

References

• T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 32, Cf. Theorem 2.10.