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

1, 2, 4, 6, 12, 24, 30, 60, 120, 180, 210, 420, 840, 1260, 2310, 4620, 9240, 13860, 27720, 30030, 60060, 120120, 180180, 360360, 510510, 1021020, 2042040, 3063060, 6126120, 9699690, 19399380, 38798760, 58198140, 116396280, 223092870, 446185740, 892371480

Offset: 1

Author

Daniel Suteu, Feb 18 2017

Keywords

• nonn

Comments

First 14 terms are similar, with A168264.

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..176 (terms 1..50 from Giovanni Resta)

Crossrefs

Cf. A000005, A126098, A168264.

Programs

Maple

A282472 := proc(n)
    option remember;
    local a,a1,rec ;
    if n = 1 then
        1;
    else
        a1 := procname(n-1) ;
        rec := numtheory[tau](a1^2)/numtheory[tau](a1) ;
        for a from a1+1 do
            if numtheory[tau](a^2)/numtheory[tau](a) > rec then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Mar 03 2017

Mathematica

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 *)

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

Perl

use ntheory qw(:all);
for (my ($n, $m) = (1, 0) ; ; ++$n) {
    my $d = divisors($n*$n) / divisors($n);
    if ($m < $d) {
        $m = $d;
        print "$n\n";
    }
}

Extensions

a(32)-a(35) from Lars Blomberg, Apr 10 2017

a(36)-a(37) from Giovanni Resta, Apr 10 2017