A057793 Integer nearest Riemann(10^n), where Riemann(x) = Sum_{k=1..infinity} mu(k)/k * Integral Log( x^(1/k) ).

5, 26, 168, 1227, 9587, 78527, 664667, 5761552, 50847455, 455050683, 4118052495, 37607910542, 346065531066, 3204941731602, 29844570495887, 279238341360977, 2623557157055978, 24739954284239494, 234057667300228940

Offset: 1

Author

Robert G. Wilson v, Nov 04 2000

Keywords

• nonn

Comments

Riemann(x) is Riemann's approximation for the number of primes less than x.

References

• John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1996, page 144-146.

Links

• Vladimir Pletser, Table of n, a(n) for n = 1..100 [a(40) corrected by _David Baugh_, Oct 11 2020]
• Eric Weisstein's World of Mathematics, Riemann Prime Counting Function

Programs

Mathematica

Rie[n_Integer] := Sum[N[LogIntegral[n^(1/k)]*MoebiusMu[k]/k, 36], {k, 1, 5!}]; Table[Round[Rie[10^n]], {n, 1, 21}]
Table[Round@N[RiemannR[10^n], 50], {n, 21}] (* Arkadiusz Wesolowski, Dec 30 2011 *)

Extensions

a(1) corrected by Chris Katscher (spatch3(AT)yahoo.com), May 25 2003

a(20) to a(100) from Vladimir Pletser, Aug 10 2013