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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 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 STATUS approved

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Last modified October 20 13:41 EDT 2019. Contains 328257 sequences. (Running on oeis4.)