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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 (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 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_k-1)+1 times, where g is 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. 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

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Last modified April 22 14:13 EDT 2019. Contains 322349 sequences. (Running on oeis4.)