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 *)
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 *)
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
KEYWORD
nonn
AUTHOR
Daniel Suteu, Feb 18 2017
STATUS
approved