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Numbers k where records occur for d(k^2)/d(k), where d(k) is A000005(k).
3

%I #49 May 06 2022 13:13:51

%S 1,2,4,6,12,24,30,60,120,180,210,420,840,1260,2310,4620,9240,13860,

%T 27720,30030,60060,120120,180180,360360,510510,1021020,2042040,

%U 3063060,6126120,9699690,19399380,38798760,58198140,116396280,223092870,446185740,892371480

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

%C First 14 terms are similar, with A168264.

%C 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 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 := proc(n)

%p option remember;

%p local a,a1,rec ;

%p if n = 1 then

%p 1;

%p else

%p a1 := procname(n-1) ;

%p rec := numtheory[tau](a1^2)/numtheory[tau](a1) ;

%p for a from a1+1 do

%p if numtheory[tau](a^2)/numtheory[tau](a) > rec then

%p return a;

%p end if;

%p end do:

%p end if;

%p end proc: # _R. J. Mathar_, Mar 03 2017

%t 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 (Perl)

%o use ntheory qw(:all);

%o for (my ($n, $m) = (1, 0) ; ; ++$n) {

%o my $d = divisors($n*$n) / divisors($n);

%o if ($m < $d) {

%o $m = $d;

%o print "$n\n";

%o }

%o }

%o (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 Cf. A000005, A126098, A168264.

%K nonn

%O 1,2

%A _Daniel Suteu_, Feb 18 2017

%E a(32)-a(35) from _Lars Blomberg_, Apr 10 2017

%E a(36)-a(37) from _Giovanni Resta_, Apr 10 2017