cp's OEIS Frontend

A036438 Integers which can be written as m*tau(m) for some m, where tau = A000005.

%I A036438 #16 Feb 01 2025 08:44:33
%S A036438 1,4,6,10,12,14,22,24,26,27,32,34,38,40,46,56,58,60,62,72,74,75,80,82,
%T A036438 84,86,88,94,104,106,108,118,120,122,132,134,136,140,142,146,147,152,
%U A036438 156,158,166,168,178,184,192,194,202,204,206,214,218,220,226,228,232
%N A036438 Integers which can be written as m*tau(m) for some m, where tau = A000005.
%C A036438 Invented by the HR concept formation program.
%H A036438 Antti Karttunen, <a href="/A036438/b036438.txt">Table of n, a(n) for n = 1..11329</a>
%H A036438 Simon Colton, <a href="http://www.cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2 (1999), Article 99.1.2.
%H A036438 Simon Colton, <a href="http://web.archive.org/web/20070831060523/http://www.dai.ed.ac.uk/homes/simonco/research/hr/">HR - Automatic Theory Formation in Pure Mathematics</a>, 1998-1999. [Wayback Machine link]
%e A036438 10 = 5 * tau(5).
%t A036438 q[k_] := AnyTrue[Divisors[k], # * DivisorSigma[0, #] == k &]; Select[Range[250], q] (* _Amiram Eldar_, Feb 01 2025 *)
%o A036438 (PARI) isok(n) = {for (k=1, n, if (k*numdiv(k) == n, return (1));); return (0);} \\ _Michel Marcus_, Dec 09 2014
%o A036438 (PARI)
%o A036438 up_to = 65536;
%o A036438 A036438list(up_to) = { my(v=vector(up_to), m = Map()); for(n=1,#v,mapput(m,n*numdiv(n),n)); my(k=0,u=0); while((k<#v)&&(u<#v), u++; if(mapisdefined(m,u), k++; v[k] = u)); vector(k,i,v[i]); };
%o A036438 v036438 = A036438list(up_to);
%o A036438 A036438(n) = v036438[n]; \\ _Antti Karttunen_, Jul 18 2020
%Y A036438 Cf. A000005, A001747, A036434.
%Y A036438 Range of A038040.
%K A036438 easy,nonn
%O A036438 1,2
%A A036438 Simon Colton (simonco(AT)cs.york.ac.uk)