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A282472 Numbers k where records occur for d(k^2)/d(k), where d(k) is A000005(k).

%I A282472 #49 May 06 2022 13:13:51
%S A282472 1,2,4,6,12,24,30,60,120,180,210,420,840,1260,2310,4620,9240,13860,
%T A282472 27720,30030,60060,120120,180180,360360,510510,1021020,2042040,
%U A282472 3063060,6126120,9699690,19399380,38798760,58198140,116396280,223092870,446185740,892371480
%N A282472 Numbers k where records occur for d(k^2)/d(k), where d(k) is A000005(k).
%C A282472 First 14 terms are similar, with A168264.
%C A282472 The quotients are (1, 3/2, 5/3, 9/4, 5/2, 21/8, 27/8, 15/4, 63/16, 25/6, 81/16, 45/8, 189/32, 25/4, 243/32, 135/16, 567/64, 75/8, 315/32, 729/64, 405/32, 1701/128, 225/16, 945/64, 2187/128, 1215/64, 5103/256, 675/32, 2835/128, 6561/256, 3645/128, 15309/512, 2025/64, 8505/256, 19683/512,...). - _Lars Blomberg_, Apr 10 2017
%H A282472 Amiram Eldar, <a href="/A282472/b282472.txt">Table of n, a(n) for n = 1..176</a> (terms 1..50 from Giovanni Resta)
%p A282472 A282472 := proc(n)
%p A282472     option remember;
%p A282472     local a,a1,rec ;
%p A282472     if n = 1 then
%p A282472         1;
%p A282472     else
%p A282472         a1 := procname(n-1) ;
%p A282472         rec := numtheory[tau](a1^2)/numtheory[tau](a1) ;
%p A282472         for a from a1+1 do
%p A282472             if numtheory[tau](a^2)/numtheory[tau](a) > rec then
%p A282472                 return a;
%p A282472             end if;
%p A282472         end do:
%p A282472     end if;
%p A282472 end proc: # _R. J. Mathar_, Mar 03 2017
%t A282472 s={}; rm=0; Do[r=DivisorSigma[0, n^2]/DivisorSigma[0, n]; If[r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^4}]; s (* _Amiram Eldar_, Jul 17 2019 *)
%o A282472 (Perl)
%o A282472 use ntheory qw(:all);
%o A282472 for (my ($n, $m) = (1, 0) ; ; ++$n) {
%o A282472     my $d = divisors($n*$n) / divisors($n);
%o A282472     if ($m < $d) {
%o A282472         $m = $d;
%o A282472         print "$n\n";
%o A282472     }
%o A282472 }
%o A282472 (PARI) lista(nn) = {rec = 0; for (n=1, nn, if ((newrec = numdiv(n^2)/numdiv(n)) > rec, rec = newrec; print1(n, ", ")););} \\ _Michel Marcus_, Feb 20 2017
%Y A282472 Cf. A000005, A126098, A168264.
%K A282472 nonn
%O A282472 1,2
%A A282472 _Daniel Suteu_, Feb 18 2017
%E A282472 a(32)-a(35) from _Lars Blomberg_, Apr 10 2017
%E A282472 a(36)-a(37) from _Giovanni Resta_, Apr 10 2017