A227730 - OEIS

%I #10 Nov 30 2014 13:25:31

%S 1,2,4,8,12,16,24,32,36,48,60,64,72,80,96,108,112,120,128,144,160,168,

%T 180,192,216,224,240,252,256,288,300,320,324,336,360,384,396,400,420,

%U 432,448,480,504,512,528,540,560,576,600,640,648,660,672,704,720,756,768,784

%N Doubly 2-densely divisible numbers.

%C Numbers n such that for each d | n, there is some 2-densely divisible (A174973) number d' such that d/2 < d' <= d.

%H Charles R Greathouse IV, <a href="/A227730/b227730.txt">Table of n, a(n) for n = 1..10000</a>

%H Terence Tao, <a href="http://terrytao.wordpress.com/2013/07/07/the-distribution-of-primes-in-doubly-densely-divisible-moduli/">The distribution of primes in doubly densely divisible moduli</a>

%o (PARI) dense(n,k)=my(d=divisors(n)); for(i=2, #d, if(d[i]>k*d[i-1], return(0))); 1

%o is(n)=my(d=select(k->dense(k,2),divisors(n))); if(!#d||2*d[#d]<n,return(0)); for(i=2, #d, if(d[i]>2*d[i-1], return(0))); 1

%Y Cf. A227731, A174973.

%K nonn

%O 1,2

%A _Charles R Greathouse IV_, Jul 23 2013