A227730 Doubly 2-densely divisible numbers.

1, 2, 4, 8, 12, 16, 24, 32, 36, 48, 60, 64, 72, 80, 96, 108, 112, 120, 128, 144, 160, 168, 180, 192, 216, 224, 240, 252, 256, 288, 300, 320, 324, 336, 360, 384, 396, 400, 420, 432, 448, 480, 504, 512, 528, 540, 560, 576, 600, 640, 648, 660, 672, 704, 720, 756, 768, 784

Offset: 1

Author

Charles R Greathouse IV, Jul 23 2013

Keywords

• nonn

Comments

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Terence Tao, The distribution of primes in doubly densely divisible moduli

Crossrefs

Cf. A227731, A174973.

Programs

PARI

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