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A191857 - 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>A191857 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A191857" 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=%2fA191857">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="A191857 - 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> A191857 </div> <div class=seqname> Second factor in happy factorization of n-th rhombic number. </div> </div> <div class=scorerefs> 6 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>3, 1, 4, 11, 5, 19, 1, 6, 27, 1, 2, 7, 20, 43, 1, 8, 51, 59, 9, 67, 1, 3, 1, 10, 83, 29, 22, 7, 2, 11, 1, 52, 107, 23, 1, 12, 123, 1, 2, 131, 5, 4, 139, 13, 1, 38, 53, 2, 163, 1, 14, 171, 25, 8, 179, 187, 1, 2, 15, 1, 100, 26, 211, 5, 54, 3, 1, 16, 227, 77</div> <div class=seqdatalinks> (<a href="/A191857/list">list</a>; <a href="/A191857/graph">graph</a>; <a href="/search?q=A191857+-id:A191857">refs</a>; <a href="/A191857/listen">listen</a>; <a href="/history?seq=A191857">history</a>; <a href="/search?q=id:A191857&fmt=text">text</a>; <a href="/A191857/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,1</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>a(n) = <a href="/A007967" title="Second factor in happy factorization of n.">A007967</a>(<a href="/A007970" title="Rhombic numbers.">A007970</a>(n)) = <a href="/A007970" title="Rhombic numbers.">A007970</a>(n) / <a href="/A191856" title="First factor in happy factorization of n-th rhombic number.">A191856</a>(n);</div> <div class=sectline>(<a href="/A191856" title="First factor in happy factorization of n-th rhombic number.">A191856</a>(n), a(n)) is a 2-happy couple;</div> <div class=sectline>notation: E in the Conway link.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Reinhard Zumkeller, <a href="/A191857/b191857.txt">Table of n, a(n) for n = 1..99</a></div> <div class=sectline>J. H. Conway, <a href="http://www.cs.uwaterloo.ca/journals/JIS/happy.html">On Happy Factorizations</a>, J. Integer Sequences, Vol. 1, 1998, #1.</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Haskell)</div> <div class=sectline>a191857 = a007967 . a007970 -- <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Oct 11 2015</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A007967" title="Second factor in happy factorization of n.">A007967</a>, <a href="/A007970" title="Rhombic numbers.">A007970</a>, <a href="/A191856" title="First factor in happy factorization of n-th rhombic number.">A191856</a>.</div> <div class=sectline>Sequence in context: <a href="/A125077" title="#4 in an infinite set of generalized Pascal's triangles with trigonometric properties.">A125077</a> <a href="/A065253" title="a(n) = 10*(A064823(n)-1) + A000796(n).">A065253</a> <a href="/A010756" title="Sum along upward diagonal of Pascal triangle from (but not including) center.">A010756</a> * <a href="/A248044" title="Least positive integer m such that m + n divides pi(m)^2 + pi(n)^2, where pi(x) denotes the number of primes not exceeding x.">A248044</a> <a href="/A153278" title="Array read by antidiagonals of higher order Fubini numbers.">A153278</a> <a href="/A010284" title="Continued fraction for cube root of 55.">A010284</a></div> <div class=sectline>Adjacent sequences: <a href="/A191854" title="First factor in happy factorization of n-th rectangular number.">A191854</a> <a href="/A191855" title="Second factor in happy factorization of n-th rectangular number.">A191855</a> <a href="/A191856" title="First factor in happy factorization of n-th rhombic number.">A191856</a> * <a href="/A191858" title="The greatest integer M for which there are no primes between M^(1+1/n) and (M+1)^(1+1/n)">A191858</a> <a href="/A191859" title="The primes created by concatenation of anti-divisors in A191647.">A191859</a> <a href="/A191860" title="First member of a pair of numbers occurring in the definition of 1-happy couples.">A191860</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>, Jun 18 2011</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>Wrong formula removed (thanks to <a href="/wiki/User:Wolfdieter_Lang">Wolfdieter Lang</a>, who pointed this out), by <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Oct 11 2015</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 February 16 07:09 EST 2025. Contains 380893 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>