cp's OEIS Frontend

A336509 Even squarefree numbers k such that d_{i+1}/d_i < 2 for all 1 < i < tau(k) - 1, where 1 = d_1 < d_2 < ... < d_tau(k) = k are the divisors of k, and tau(k) is their number (A000005).

%I A336509 #7 Jul 26 2020 02:33:49
%S A336509 6,30,210,330,390,510,570,690,870,2310,2730,3570,3990,4290,4830,5610,
%T A336509 6090,6270,6510,6630,7410,7590,7770,8610,8970,9030,9570,9690,9870,
%U A336509 10230,11130,11310,11730,12090,12210,12390,12810,13110,13530,14070,14190,14430,14790,14910
%N A336509 Even squarefree numbers k such that d_{i+1}/d_i < 2 for all 1 < i < tau(k) - 1, where 1 = d_1 < d_2 < ... < d_tau(k) = k are the divisors of k, and tau(k) is their number (A000005).
%C A336509 Thompson (2012) called these numbers "strictly 2-dense numbers" and proved that they are all phi-practical numbers (A260653).
%H A336509 Amiram Eldar, <a href="/A336509/b336509.txt">Table of n, a(n) for n = 1..10000</a>
%H A336509 Lola Thompson, <a href="https://doi.org/10.1016/j.jnt.2011.10.005">Polynomials with divisors of every degree</a>, Journal of Number Theory, Vol. 132, No. 5 (2012), pp. 1038-1053.
%H A336509 Lola Thompson, <a href="https://doi.org/10.5802/jtnb.866">Variations on a question concerning the degrees of divisors of x^n - 1</a>, Journal de Théorie des Nombres de Bordeaux, Vol. 26, No. 1 (2014), pp. 253-267.
%t A336509 sdQ[n_] := SquareFreeQ[n] && Length[(d = Rest @ Most @ Divisors[n])] >0 && Max[Rest[d]/Most[d]] < 2; Select[Range[2, 15000, 2], sdQ]
%Y A336509 Subsequence of A174973 and A260653.
%Y A336509 Cf. A000005, A005117, A039956.
%K A336509 nonn
%O A336509 1,1
%A A336509 _Amiram Eldar_, Jul 23 2020