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A048656 a(n) is the number of unitary (and also of squarefree) divisors of n!. 10
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; text; internal format)
OFFSET

1,2

COMMENTS

Let K(n) be the 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

LINKS

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

Index to divisibility sequences

EXAMPLE

n=7, n! = 5040 = 16*9*5*7 with 4 distinct prime factors, so a(7) = A034444(7!) = 16.

PROG

(PARI) a(n)=2^primepi(n) \\ Charles R Greathouse IV, Apr 07 2012

CROSSREFS

A001221(n!)=A000720(n) so a(n)=A034444(n!)=2^(A000720(n)).

Sequence in context: A166632 A116596 A248692 * A107848 A285273 A188824

Adjacent sequences:  A048653 A048654 A048655 * A048657 A048658 A048659

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified August 15 09:12 EDT 2018. Contains 313756 sequences. (Running on oeis4.)