A282531 - OEIS

%I #21 Jun 10 2024 14:28:13

%S 1,11,23,47,59,167,179,239,359,719,839,1259,2879,3359,5039,7559,10079,

%T 21839,33599,35279,37799,55439,100799,110879,166319,262079,327599,

%U 415799,665279,831599,1081079,1441439,2827439,3326399,4989599,6320159,6486479,10533599

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

%C This sequence is infinite (Schinzel, 1954). - _Amiram Eldar_, Apr 18 2024

%H Amiram Eldar, <a href="/A282531/b282531.txt">Table of n, a(n) for n = 1..71</a> (terms 1..52 from Daniel Suteu)

%H Andrzej Schinzel, <a href="https://doi.org/10.5486/PMD.1954.3.3-4.11">Sur une propriété du nombre de diviseurs</a>, Publ. Math. (Debrecen), Vol. 3 (1954), pp. 261-262.

%t 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 *)

%t Module[{nn=840000},DeleteDuplicates[Thread[{Range[nn-1],#[[2]]/#[[1]]&/@Partition[ DivisorSigma[ 0,Range[nn]],2,1]}],GreaterEqual[#1[[2]],#2[[2]]]&]][[;;,1]] (* The program generates the first 30 terms of the sequence. *) (* _Harvey P. Dale_, Jun 10 2024 *)

%o (Perl)

%o use ntheory qw(:all);

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

%o     my $d = divisors($n+1) / divisors($n);

%o     if ($m < $d) {

%o         $m = $d;

%o         print "$n\n";

%o     }

%o }

%o (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

%Y Cf. A000005, A372092.

%K nonn

%O 1,2

%A _Daniel Suteu_, Feb 18 2017