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A048656
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Number of unitary (and also of squarefree) divisors of n!.
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8
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1, 2, 4, 4, 8, 8, 16, 16, 16, 16, 32, 32, 64, 64, 64, 64, 128, 128, 256, 256, 256, 256, 512, 512, 512, 512, 512, 512, 1024, 1024, 2048, 2048, 2048, 2048, 2048, 2048, 4096, 4096, 4096, 4096, 8192, 8192, 16384, 16384, 16384, 16384, 32768, 32768, 32768, 32768
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Let K(n) = field that is generated over the rationals Q by adjoining the square roots of the numbers 1,2,3,...,n i.e. K(n) = Q(sqrt(1),sqrt(2),...,sqrt(n)); a(n) is the degree of this field over Q. - Avi Peretz (njk(AT)netvision.net.il), Mar 20 2001
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EXAMPLE
| n=7, n!=5040=16*9*5*7 with 4 distinct prime factors, so A034444(7!)=16.
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CROSSREFS
| A001221(n!)=A000720(n) so a(n)=A034444(n!)=2^(A000720(n)).
Sequence in context: A188112 A166632 A116596 * A107848 A188824 A181212
Adjacent sequences: A048653 A048654 A048655 * A048657 A048658 A048659
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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