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

1,1

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

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 *)

Crossrefs

Sequence in context: A349882 A209672 A367041 * A090226 A355672 A356597

Adjacent sequences: A057790 A057791 A057792 * A057794 A057795 A057796

Keyword

nonn

Author

Robert G. Wilson v, Nov 04 2000

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

Status

approved