A047783 a(n) = floor(Li(n)).

1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 238.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 2..1000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A047784 (round), A047785 (ceiling).

Programs

Magma

[Floor(LogIntegral(n)): n in [2..80]]; // G. C. Greubel, May 17 2019

Mathematica

Array[Floor[LogIntegral[#]] &, 70, 2] (* Robert G. Wilson v, Feb 23 2017 *)

PARI

vector(80, n, n++; floor(real(-eint1(-log(n)))) ) \\ G. C. Greubel, May 17 2019

Sage

[floor(li(n)) for n in (2..80)] # G. C. Greubel, May 17 2019

Formula

a(n) = floor(logarithmic integral(n)). - G. C. Greubel, May 17 2019