A279373 - OEIS

%I #14 Nov 05 2019 06:56:05

%S 1,2,8,9,12,18,24,36,40,56,60,72,80,84,180,225,240,252,288,360,396,

%T 441,448,450,504,560,600,625,672,720,792,880,882,936,1040,1056,1200,

%U 1248,1250,1260,1344,1408,1440,1620,1664,1680,1800,1980,2000,2016,2025,2160,2176,2240,2340,2640,2700,2772,3120,3168

%N Numbers n such that number of divisors of n divides n and at the same time the least number having exactly n divisors is divisible by n.

%C Intersection of A033950 and A262981.

%H Amiram Eldar, <a href="/A279373/b279373.txt">Table of n, a(n) for n = 1..267</a>

%H A. Bundy, Simon Colton, T. Walsh, <a href="http://www.doc.ic.ac.uk/~sgc/papers/bundy_ecai98.pdf">HR - A system for Machine Discovery in Finite Algebras</a>, ECAI 1998.

%H S. Colton, <a href="http://www.cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2, 1999, #2.

%H S. Colton, <a href="http://www.dai.ed.ac.uk/homes/simonco/research/hr/">HR - Automatic Theory Formation in Pure Mathematics</a>

%H Robert E. Kennedy and Curtis N. Cooper, <a href="http://downloads.hindawi.com/journals/ijmms/1990/717323.pdf">Tau numbers, natural density and Hardy and Wright's Theorem 437</a>, International Journal of Mathematics and Mathematical Sciences, 13:2 (1990), pp. 383-386.

%H Claudia Spiro, <a href="http://dx.doi.org/10.1016/0022-314X(85)90012-5">How often is the number of divisors of n a divisor of n?</a>, J. Number Theory 21 (1985), no. 1, 81-100.

%H Vladimir Letsko, <a href="http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_216">Mathematical Marathon, Problem 216</a> (in Russian)

%e 8 is in the sequence because 8 is divisible by tau(8) and at the same time 8 divides 24 which is the least number having exactly 8 divisors.

%t Function[s, Select[TakeWhile[#, KeyExistsQ[s, #] &], Divisible[Lookup[s, #], #] &] &@ Select[Range@ 3000, Divisible[#, DivisorSigma[0, #]] &]]@ Map[First, KeySort@ PositionIndex@ Table[DivisorSigma[0, n], {n, 10^7}]] (* _Michael De Vlieger_, Dec 11 2016, Version 10 *)

%Y Cf. A000005, A005179, A033950, A262981, A262983.

%K nonn

%O 1,2

%A _Vladimir Letsko_, Dec 11 2016