%I #17 Apr 28 2019 05:36:12

%S 2,2,4,4,8,8,8,16,16,16,16,32,32,32,64,64,64,64,128,128,128,128,128,

%T 256,256,256,256,512,512,512,512,512,1024,1024,1024,1024,1024,2048,

%U 2048,2048,2048,2048,4096,4096,4096,4096,4096,4096,8192,8192,8192,8192

%N Maximal value of number of unitary divisors (see A034444) for integers in binary order range of n.

%C Q_k the k-th primorial number (A002110) is the smallest positive integer whose number of unitary divisors (A034444) is 2^k. Thus the binary orders (A029837) of primorial numbers (A045716) determine the maximal values of unitary divisors in binary order ranges.

%H Charles R Greathouse IV, <a href="/A046971/b046971.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%F 2^k occurs in the sequence g(Q_k) - g(Q_k-1)+1 times, where g is the binary order and Q_k is the k-th primorial number.

%e 128 occurs in the sequence from index 19 and 23 inclusively (5 times) because the 7th primorial number Q_7=510510 has binary order 19 and Q_8, the next one is 9699690 has binary order 24 (it is between 2^23 and 2^24).

%o (PARI) v=List([2]);n=0;P=p=2;forprime(q=3,97, n++;for(i=1, log(P*q)\log(2)-log(P)\log(2), listput(v,1<<n));P*=p=q);Vec(v) \\ _Charles R Greathouse IV_, Apr 08 2012

%Y Cf. A002110, A029837, A034444, A045716.

%K nonn

%O 1,1

%A _Labos Elemer_