

A046971


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


2



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
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OFFSET

1,1


COMMENTS

Q_k the kth primorial number (A002110) is the smallest positive integer such that its number of unitary divisors (A034444) is 2^k. Thus the binary orders (A029837) of primorial numbers (A045716) determines 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_k1)+1 times, where g is binary order and Q_k is the kth 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. A029837, A034444, A002110, A045716.
Sequence in context: A190172 A287293 A059867 * A051754 A108747 A116931
Adjacent sequences: A046968 A046969 A046970 * A046972 A046973 A046974


KEYWORD

nonn


AUTHOR

Labos Elemer


STATUS

approved



