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.

A322713 a(n) = numerator of the Riemann prime counting function for 10^n.

This page as a plain text file.
%I A322713 #11 Feb 16 2025 08:33:57
%S A322713 0,16,428,445273,56175529,991892879,18296822833013,3559637526370229,
%T A322713 6427431691337929,14804074778750628149,9387415960571046321167,
%U A322713 594663752918349842404169,200936708396848319452718531,296345083061712053722716462103,30189234512048649753828116713823
%N A322713 a(n) = numerator of the Riemann prime counting function for 10^n.
%H A322713 Daniel Suteu, <a href="/A322713/b322713.txt">Table of n, a(n) for n = 0..27</a>
%H A322713 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannPrimeCountingFunction.html">Riemann Prime Counting Function</a>
%F A322713 a(n) = A096624(10^n).
%F A322713 a(n) = numerator of Sum_{k=1..floor(log_2(10^n))} pi(floor(10^(n/k)))/k, where pi(x) is the prime counting function A000720.
%e A322713 0, 16/3, 428/15, 445273/2520, 56175529/45045, 991892879/102960, 18296822833013/232792560, ...
%o A322713 (PARI) a(n) = numerator(sum(k=1, logint(10^n, 2), primepi(sqrtnint(10^n, k))/k));
%Y A322713 The corresponding denominators are A322714.
%Y A322713 Cf. A000720, A096624.
%K A322713 frac,nonn
%O A322713 0,2
%A A322713 _Daniel Suteu_, Dec 24 2018