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A176670 - 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>A176670 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A176670\/internal" 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=%2fA176670%2finternal">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="A176670 - 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> <a href="/A176670">A176670</a> </div> <div class=seqname> Composite numbers having the same digits as their prime factors (with multiplicity), excluding zero digits. </div> </div> <div class=scorerefs> 12 </div> </div> <div> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%I #55 Feb 16 2025 08:33:12 </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%S 1111,1255,12955,17482,25105,28174,51295,81229,91365,100255,101299, </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%T 105295,107329,110191,110317,117067,124483,127417,129595,132565, </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%U 137281,145273,146137,149782,163797,171735,174082,174298,174793,174982,193117,208174,210181,217894 </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%N Composite numbers having the same digits as their prime factors (with multiplicity), excluding zero digits. </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%C Subsequence of A006753 (Smith numbers). </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%C These numbers still need a better name. - _Ely Golden_, Dec 25 2016 </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%C Terms of this sequence never have more zero digits than their prime factors. - _Ely Golden_, Jan 10 2017 </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%H Ely Golden, <a href="/A176670/b176670.txt">Table of n, a(n) for n = 1..10000</a> [Terms 1 through 2113 were computed by Paul Weisenhorn; and terms 2114 to 10000 by Ely Golden, Nov 30 2016] </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%H Ely Golden, <a href="/A176670/a176670_1.sagews.txt">Smith number sequence generator optimized for A176670</a> </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%H Ely Golden, <a href="/A280827/a280827.txt">Proof that A280827(n)>=0 for all n>1</a> </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%H Eric W. Weisstein, <a href="https://mathworld.wolfram.com/SmithNumber.html">Smith Number</a> </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%e n = 25105 = 5*5021; both n and the factorization of n have digits 1, 2, 5, 5; sorted and excluding zeros. </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%e n = 110191 = 101*1091; both n and the factorization of n have digits 1, 1, 1, 1, 9; sorted and excluding zeros. </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%e n = 171735 = 3*5*107*107; both n and the factorization of n have digits 1, 1, 3, 5, 7, 7; sorted and excluding zeros. </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%t fQ[n_] := Block[{id = Sort@ IntegerDigits@ n, s = Sort@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@ n]}, While[ id[[1]] == 0, id = Drop[id, 1]]; While[ s[[1]] == 0, s = Drop[s, 1]]; n > 1 && ! PrimeQ@ n && s == id]; Select[ Range@ 200000, fQ] </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%t Select[Range[2*10^5], Function[n, And[CompositeQ@ n, Sort@ DeleteCases[#, 0] &@ IntegerDigits@ n == Sort@ DeleteCases[#, 0] &@ Flatten@ Map[IntegerDigits@ ConstantArray[#1, #2] & @@ # &, FactorInteger@ n]]]] (* _Michael De Vlieger_, Dec 10 2016 *) </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%o (Python) </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%o from sympy import factorint, flatten </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%o def sd(n): return sorted(str(n).replace('0', '')) </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%o def ok(n): </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%o f = factorint(n) </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%o return sum(f[p] for p in f) > 1 and sd(n) == sorted(flatten(sd(p)*f[p] for p in f)) </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%o print(list(filter(ok, range(220000)))) # _Michael S. Branicky_, Apr 22 2021 </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%Y Cf. A006753. </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%K nonn,base </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%O 1,1 </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt>%A _Paul Weisenhorn_, Apr 23 2010 </tt></p> <p style="text-indent: -2em; margin-left: 2em; margin-top: 0; margin-bottom: 0;"><tt></tt></p> </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 March 16 16:38 EDT 2025. Contains 381811 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>