A282531 Numbers k where records occur for d(k+1)/d(k), where d(k) is A000005(k).

1, 11, 23, 47, 59, 167, 179, 239, 359, 719, 839, 1259, 2879, 3359, 5039, 7559, 10079, 21839, 33599, 35279, 37799, 55439, 100799, 110879, 166319, 262079, 327599, 415799, 665279, 831599, 1081079, 1441439, 2827439, 3326399, 4989599, 6320159, 6486479, 10533599

Offset

1,2

Comments

This sequence is infinite (Schinzel, 1954). - Amiram Eldar, Apr 18 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..71 (terms 1..52 from Daniel Suteu)

Andrzej Schinzel, Sur une propriété du nombre de diviseurs, Publ. Math. (Debrecen), Vol. 3 (1954), pp. 261-262.

Mathematica

seq[kmax_] := Module[{d1 = 1, d2, rm = 0, r, s = {}}, Do[d2 = DivisorSigma[0, k]; r = d2 / d1; If[r > rm, rm = r; AppendTo[s, k-1]]; d1 = d2, {k, 2, kmax}]; s]; seq[10^6] (* Amiram Eldar, Apr 18 2024 *)

Prog

(Perl)
use ntheory qw(:all);
for (my ($n, $m) = (1, 0) ; ; ++$n) {
    my $d = divisors($n+1) / divisors($n);
    if ($m < $d) {
        $m = $d;
        print "$n\n";
    }
}
(PARI) lista(kmax) = {my(d1 = 1, d2, rm = 0, r); for(k = 2, kmax, d2 = numdiv(k); r = d2 / d1; if(r > rm, rm = r; print1(k-1, ", ")); d1 = d2); } \\ Amiram Eldar, Apr 18 2024

Crossrefs

Cf. A000005, A372092.

Sequence in context: A073024 A359387 A161897 * A309851 A145994 A217047

Adjacent sequences: A282528 A282529 A282530 * A282532 A282533 A282534

Keyword

nonn,changed

Author

Daniel Suteu, Feb 18 2017

Status

approved