CINXE.COM
A064646 - OEIS
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>A064646 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A064646" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fA064646">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="A064646 - OEIS"></a> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A064646 </div> <div class=seqname> Numerators of partial sums of reciprocals of primorial numbers. </div> </div> <div class=scorerefs> 2 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 7, 74, 543, 10589, 120009, 3420257, 4767631, 2281311434, 141441308909, 51307141467, 3301022547923, 200573000466191, 433638827007904943, 328326540448842314, 31534618884970203647, 13785884222546140694347</div> <div class=seqdatalinks> (<a href="/A064646/list">list</a>; <a href="/A064646/graph">graph</a>; <a href="/search?q=A064646+-id:A064646">refs</a>; <a href="/A064646/listen">listen</a>; <a href="/history?seq=A064646">history</a>; <a href="/search?q=id:A064646&fmt=text">text</a>; <a href="/A064646/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,2</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A064646/b064646.txt">Table of n, a(n) for n=1..18.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>n=5, Sum[1/q(j)],j=1..5 = 1/2+1/6+1/30+1/210+1/2310= (1155+385+77+11+1)/2310=1629/2310=543/770, a(5)=543</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>q[x_] := Apply[Times, Table[Prime[j], {j, 1, x}]] a(n)=Numerator[Apply[Plus, Table[1/q[w], {w, 1, n}]]]</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline><a href="/A002110" title="Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.">A002110</a>.</div> <div class=sectline>Sequence in context: <a href="/A119811" title="Numerators of the convergents to the continued fraction for the constant A119809 defined by binary sums involving Beatty seq...">A119811</a> <a href="/A319621" title="Number of non-isomorphic connected antichain covers of n vertices by distinct sets whose dual is also an antichain of (not n...">A319621</a> <a href="/A167526" title="Prime factors of the speed of light in a vacuum, c = 299792458 (m/s).">A167526</a> * <a href="/A366407" title="G.f. A(x) satisfies A(x) = (1 + x / A(x)^(9/2)) / (1 - x).">A366407</a> <a href="/A144905" title="a(0) = 1; thereafter a(n) = A105749(n)/n.">A144905</a> <a href="/A349500" title="a(n) is the least number k such that A349474(k) = A349474(k+1) = n, or -1 if no such k exists.">A349500</a></div> <div class=sectline>Adjacent sequences: <a href="/A064643" title="Bidirectional 'Delannoy' variation of the Boustrophedon transform applied to all 1's sequence: Fill an triangular array in a...">A064643</a> <a href="/A064644" title="Array defined in A064643 read from left to right (cf. A107783).">A064644</a> <a href="/A064645" title="Table where the entry (n,k) (n >= 0, k >= 0) gives number of Motzkin paths of the length n with the minimum peak width of k.">A064645</a> * <a href="/A064647" title="Denominators of partial sums of reciprocals of primorial numbers.">A064647</a> <a href="/A064648" title="Decimal expansion of sum of reciprocals of primorial numbers: 1/2 + 1/6 + 1/30 + 1/210 + ...">A064648</a> <a href="/A064649" title="Row sums of the table A047916.">A064649</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="numerators or denominators of sequence of rationals">frac</span>,<span title="a sequence of nonnegative numbers">nonn</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Labos_Elemer">Labos Elemer</a>, Oct 04 2001</div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified November 24 02:48 EST 2024. Contains 378053 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>