cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A309943 Numbers k such that k * d(k) > j * d(j) for all j < k, where d(k) is the number of divisors of k (A000005).

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%I A309943 #12 Aug 24 2019 14:30:29
%S A309943 1,2,3,4,6,8,10,12,16,18,20,24,30,36,42,48,60,72,84,90,96,108,120,144,
%T A309943 168,180,210,216,240,288,300,336,360,420,480,504,540,600,630,660,672,
%U A309943 720,840,1008,1080,1200,1260,1440,1680,1980,2016,2100,2160,2520,3120
%N A309943 Numbers k such that k * d(k) > j * d(j) for all j < k, where d(k) is the number of divisors of k (A000005).
%C A309943 Differs from A002093 for n >= 41.
%C A309943 Nicolas asks if there are infinitely many terms of this sequence that are not largely composite (A067128).
%H A309943 Amiram Eldar, <a href="/A309943/b309943.txt">Table of n, a(n) for n = 1..457</a>
%H A309943 Jean-Louis Nicolas, <a href="http://doi.org/10.4064/aa-49-4-395-412">Nombres hautement composés</a>, Acta Arithmetica, Vol. 49 (1988), pp. 395-412, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa49/aa4946.pdf">alternative link</a>. See p. 411.
%t A309943 s = {}; dm = 0; Do[d1 = n * DivisorSigma[0, n]; If[d1 > dm, dm = d1; AppendTo[s, n]], {n, 1, 10^4}]; s
%Y A309943 Cf. A000005, A002093, A038040, A067128.
%K A309943 nonn
%O A309943 1,2
%A A309943 _Amiram Eldar_, Aug 24 2019