A046971 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index to divisibility sequences

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.

EXAMPLE

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).

PROG

(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

CROSSREFS

Cf. A002110, A029837, A034444, A045716.

Sequence in context: A287293 A059867 A359182 * A051754 A108747 A116931

Adjacent sequences: A046968 A046969 A046970 * A046972 A046973 A046974

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved