cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A057793 #34 Feb 16 2025 08:32:43
%S A057793 5,26,168,1227,9587,78527,664667,5761552,50847455,455050683,
%T A057793 4118052495,37607910542,346065531066,3204941731602,29844570495887,
%U A057793 279238341360977,2623557157055978,24739954284239494,234057667300228940
%N A057793 Integer nearest Riemann(10^n), where Riemann(x) = Sum_{k=1..infinity} mu(k)/k * Integral Log( x^(1/k) ).
%C A057793 Riemann(x) is Riemann's approximation for the number of primes less than x.
%D A057793 John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1996, page 144-146.
%H A057793 Vladimir Pletser, <a href="/A057793/b057793.txt">Table of n, a(n) for n = 1..100</a> [a(40) corrected by _David Baugh_, Oct 11 2020]
%H A057793 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannPrimeCountingFunction.html">Riemann Prime Counting Function</a>
%t A057793 Rie[n_Integer] := Sum[N[LogIntegral[n^(1/k)]*MoebiusMu[k]/k, 36], {k, 1, 5!}]; Table[Round[Rie[10^n]], {n, 1, 21}]
%t A057793 Table[Round@N[RiemannR[10^n], 50], {n, 21}] (* _Arkadiusz Wesolowski_, Dec 30 2011 *)
%K A057793 nonn
%O A057793 1,1
%A A057793 _Robert G. Wilson v_, Nov 04 2000
%E A057793 a(1) corrected by Chris Katscher (spatch3(AT)yahoo.com), May 25 2003
%E A057793 a(20) to a(100) from _Vladimir Pletser_, Aug 10 2013