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A282531
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Numbers k where records occur for d(k+1)/d(k), where d(k) is A000005(k).
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4
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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
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OFFSET
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1,2
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COMMENTS
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This sequence is infinite (Schinzel, 1954). - Amiram Eldar, Apr 18 2024
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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