A047784 Nearest integer to Li(n).

1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 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, 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

• G. C. Greubel, Table of n, a(n) for n = 2..10000
• 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. A047783 (floor), A047785 (ceiling).

Programs

Magma

[Round(LogIntegral(n)): n in [2..80]]; // G. C. Greubel, May 16 2019

Mathematica

Table[Round[LogIntegral[n]], {n, 2, 80}] (* G. C. Greubel, May 16 2019 *)

PARI

vector(80, n, n++; round(real(-eint1(-log(n)))) ) \\ G. C. Greubel, May 16 2019

Sage

[round(li(n)) for n in (2..80)] # G. C. Greubel, May 16 2019

Formula

a(n) = round(logarithmic integral(n)). - G. C. Greubel, May 16 2019