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A046971
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Maximal value of number of unitary divisors (see A034444) for integers in binary order range of n.
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1
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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; internal format)
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OFFSET
| 1,1
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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.
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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
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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).
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CROSSREFS
| Cf. A029837, A034444, A002110, A045716.
Sequence in context: A120541 A190172 A059867 * A051754 A108747 A116931
Adjacent sequences: A046968 A046969 A046970 * A046972 A046973 A046974
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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