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).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Cf. A000005, A005117, A039956.

Sequence in context: A362375 A369959 A057896 * A147779 A054721 A074111

Adjacent sequences: A336506 A336507 A336508 * A336510 A336511 A336512

Keyword

nonn

Author

Amiram Eldar, Jul 23 2020

Status

approved