CINXE.COM
A122408 - 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>A122408 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A122408" 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=%2fA122408">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="A122408 - 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> A122408 </div> <div class=seqname> Numbers n such that <a href="/A067824" title="a(1) = 1; for n > 1, a(n) = 1 + Sum_{0 < d < n, d|n} a(d).">A067824</a>(n) = n. </div> </div> <div class=scorerefs> 6 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 4, 6, 8, 16, 32, 40, 64, 128, 224, 256, 264, 512, 1024, 2048, 4096, 5632, 8192, 16384, 26624, 32768, 65536, 72192, 131072, 154752, 262144, 524288, 557056, 1048576, 2072576, 2097152, 2490368, 4194304, 5537792, 8388608, 10518528, 16777216, 33554432, 48234496</div> <div class=seqdatalinks> (<a href="/A122408/list">list</a>; <a href="/A122408/graph">graph</a>; <a href="/search?q=A122408+-id:A122408">refs</a>; <a href="/A122408/listen">listen</a>; <a href="/history?seq=A122408">history</a>; <a href="/search?q=id:A122408&fmt=text">text</a>; <a href="/A122408/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>Amiram Eldar, <a href="/A122408/b122408.txt">Table of n, a(n) for n = 1..100</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline><a href="/A002033" title="Number of perfect partitions of n.">A002033</a>(a(n)) = <a href="/A074206" title="Kalm谩r's [Kalmar's] problem: number of ordered factorizations of n.">A074206</a>(a(n)) = a(n)/2.</div> <div class=sectline><a href="/A067824" title="a(1) = 1; for n > 1, a(n) = 1 + Sum_{0 < d < n, d|n} a(d).">A067824</a>(a(n)) = a(n).</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>m=40, the proper divisors of 40 are 1, 2, 4, 5, 8, 10 and 20:</div> <div class=sectline><a href="/A067824" title="a(1) = 1; for n > 1, a(n) = 1 + Sum_{0 < d < n, d|n} a(d).">A067824</a>(40) = 1+Sum(<a href="/A067824" title="a(1) = 1; for n > 1, a(n) = 1 + Sum_{0 < d < n, d|n} a(d).">A067824</a>(d): 1<=d<40) = 1+(1+2+4+2+8+6+16) = 40, therefore 40 is a term.</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline><a href="/A000079" title="Powers of 2: a(n) = 2^n.">A000079</a> is a subsequence.</div> <div class=sectline>Cf. <a href="/A002033" title="Number of perfect partitions of n.">A002033</a>, <a href="/A067824" title="a(1) = 1; for n > 1, a(n) = 1 + Sum_{0 < d < n, d|n} a(d).">A067824</a>, <a href="/A074206" title="Kalm谩r's [Kalmar's] problem: number of ordered factorizations of n.">A074206</a>, <a href="/A163272" title="Numbers k such that k = A074206(k), the number of ordered factorizations of k.">A163272</a>.</div> <div class=sectline>Sequence in context: <a href="/A368325" title="Union of primorials and powers of 2.">A368325</a> <a href="/A324579" title="Numbers n for which n*A276086(n) is a product of primorial numbers (is a term of A025487).">A324579</a> <a href="/A271520" title="Domination number of the n-folded cube graph.">A271520</a> * <a href="/A326037" title="Heinz numbers of uniform perfect integer partitions.">A326037</a> <a href="/A100055" title="Where records occur in A100053.">A100055</a> <a href="/A334031" title="The smallest number whose unsorted prime signature is the reversed n-th composition in standard order.">A334031</a></div> <div class=sectline>Adjacent sequences: <a href="/A122405" title="Numbers of the form Product_i b_i^e_i, where the b_i are all distinct values > 1 and the e_i are a permutation of the b_i.">A122405</a> <a href="/A122406" title="Numbers of the form Product_i p_i^e_i, where the p_i are distinct primes and the e_i are a permutation of the p_i.">A122406</a> <a href="/A122407" title="Expansion of q^(-2/3) * b(q) * b(q^2) * c(q^2) / 3 in powers of q where b(), c() are cubic AGM theta functions.">A122407</a> * <a href="/A122409" title="Numbers k such that there is no cube between k^2 and (k+1)^2.">A122409</a> <a href="/A122410" title="a(n) = sum of j's for those k's, 1 <= k <= n, where gcd(k,n) = p^j, p = prime.">A122410</a> <a href="/A122411" title="a(n) is the sum of primes p for those k's, 2 <= k <= n, where gcd(k,n) = p^j > 1. (a(1) = 0.)">A122411</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><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:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Sep 03 2006</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>More terms from <a href="/wiki/User:Amiram_Eldar">Amiram Eldar</a>, Aug 31 2019</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 April 10 10:17 EDT 2025. Contains 382671 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>