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A340698 - 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>A340698 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A340698" 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=%2fA340698">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="A340698 - 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> A340698 </div> <div class=seqname> a(n) is the position of n^2 in the list of perfect powers. </div> </div> <div class=scorerefs> 2 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 18, 19, 21, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 59, 62, 63, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85</div> <div class=seqdatalinks> (<a href="/A340698/list">list</a>; <a href="/A340698/graph">graph</a>; <a href="/search?q=A340698+-id:A340698">refs</a>; <a href="/A340698/listen">listen</a>; <a href="/history?seq=A340698">history</a>; <a href="/search?q=id:A340698&fmt=text">text</a>; <a href="/A340698/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>Hugo Pfoertner, <a href="/A340698/b340698.txt">Table of n, a(n) for n = 1..10000</a></div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline><a href="/A340698" title="a(n) is the position of n^2 in the list of perfect powers.">A340698</a>[n_] :=</div> <div class=sectline> First @@ Position[</div> <div class=sectline> Join[{1},</div> <div class=sectline> Select[Range[n^2], GCD @@ FactorInteger[#][[All, 2]] > 1 &]],</div> <div class=sectline> n^2];</div> <div class=sectline>Table[<a href="/A340698" title="a(n) is the position of n^2 in the list of perfect powers.">A340698</a>[n], {n, 1, 67}] (* <a href="/wiki/User:Robert_P._P._McKone">Robert P. P. McKone</a>, Jan 17 2021 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) ispwr(n) = ispower(n) || (n==1); \\ <a href="/A001597" title="Perfect powers: m^k where m > 0 and k >= 2.">A001597</a></div> <div class=sectline>Vec(select(issquare, select(ispwr, [1..5000]), 1)) \\ <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Jan 18 2021</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A000290" title="The squares: a(n) = n^2.">A000290</a>, <a href="/A001597" title="Perfect powers: m^k where m > 0 and k >= 2.">A001597</a>, <a href="/A340699" title="a(n) is the position of n^3 in the list of perfect powers.">A340699</a>.</div> <div class=sectline>Sequence in context: <a href="/A343585" title="a(n) = A081411(n) mod prime(n+1).">A343585</a> <a href="/A153242" title="Positions of general trees in A014486 whose degree is not one.">A153242</a> <a href="/A143070" title="A positive integer n is included if the number of 0's in the binary representation of n is a power of 2 (including being pos...">A143070</a> * <a href="/A206926" title="Numbers such that the number of contiguous palindromic bit patterns in their binary representation is minimal (for a given n...">A206926</a> <a href="/A005528" title="St酶rmer numbers or arc-cotangent irreducible numbers: numbers k such that the largest prime factor of k^2 + 1 is >= 2*k.">A005528</a> <a href="/A211030" title="Sum of all parts in the structure of the shell model of partitions of A135010 after n-th stage.">A211030</a></div> <div class=sectline>Adjacent sequences: <a href="/A340695" title="a(n) is the next perfect power after the earliest occurrence of n consecutive perfect powers, all of which are squares with ...">A340695</a> <a href="/A340696" title="Lower of a pair of adjacent perfect powers x^p and y^q with p, q >= 4.">A340696</a> <a href="/A340697" title="Upper of a pair of adjacent perfect powers x^p and y^q with p, q >= 4.">A340697</a> * <a href="/A340699" title="a(n) is the position of n^3 in the list of perfect powers.">A340699</a> <a href="/A340700" title="Lower of a pair of adjacent perfect powers, both with exponents > 2.">A340700</a> <a href="/A340701" title="Upper of a pair of adjacent perfect powers, both with exponents > 2.">A340701</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:Hugo_Pfoertner">Hugo Pfoertner</a>, Jan 17 2021</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 19:03 EST 2024. Contains 378083 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>