A046971 Maximal value of number of unitary divisors (see A034444) for integers in binary order range of n.

2, 2, 4, 4, 8, 8, 8, 16, 16, 16, 16, 32, 32, 32, 64, 64, 64, 64, 128, 128, 128, 128, 128, 256, 256, 256, 256, 512, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 1024, 2048, 2048, 2048, 2048, 2048, 4096, 4096, 4096, 4096, 4096, 4096, 8192, 8192, 8192, 8192

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

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.

Examples

			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).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index to divisibility sequences

Crossrefs

Cf. A002110, A029837, A034444, A045716.

Programs

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<Charles R Greathouse IV, Apr 08 2012

Formula

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.