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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).
1
6, 30, 210, 330, 390, 510, 570, 690, 870, 2310, 2730, 3570, 3990, 4290, 4830, 5610, 6090, 6270, 6510, 6630, 7410, 7590, 7770, 8610, 8970, 9030, 9570, 9690, 9870, 10230, 11130, 11310, 11730, 12090, 12210, 12390, 12810, 13110, 13530, 14070, 14190, 14430, 14790, 14910
OFFSET
1,1
COMMENTS
Thompson (2012) called these numbers "strictly 2-dense numbers" and proved that they are all phi-practical numbers (A260653).
LINKS
Lola Thompson, Polynomials with divisors of every degree, Journal of Number Theory, Vol. 132, No. 5 (2012), pp. 1038-1053.
Lola Thompson, Variations on a question concerning the degrees of divisors of x^n - 1, Journal de Théorie des Nombres de Bordeaux, Vol. 26, No. 1 (2014), pp. 253-267.
MATHEMATICA
sdQ[n_] := SquareFreeQ[n] && Length[(d = Rest @ Most @ Divisors[n])] >0 && Max[Rest[d]/Most[d]] < 2; Select[Range[2, 15000, 2], sdQ]
CROSSREFS
Subsequence of A174973 and A260653.
Sequence in context: A362375 A369959 A057896 * A147779 A054721 A374660
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 23 2020
STATUS
approved