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A090616
Exponent of highest power of 4 dividing n!.
10
0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 7, 7, 8, 8, 9, 9, 9, 9, 11, 11, 11, 11, 12, 12, 13, 13, 15, 15, 16, 16, 17, 17, 17, 17, 19, 19, 19, 19, 20, 20, 21, 21, 23, 23, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28, 28, 31, 31, 32, 32, 33, 33, 33, 33, 35, 35, 35, 35, 36
OFFSET
0,7
LINKS
FORMULA
a(n) = A090622(n, 4) = floor(A011371(n)/2) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/2).
a(n) = A235127(n!). - R. J. Mathar, Jul 08 2021
EXAMPLE
a(6)=2 since 6! = 720 = 4^2 * 45.
MATHEMATICA
IntegerExponent[Range[0, 100]!, 4] (* Vincenzo Librandi, Mar 10 2013 *)
PROG
(PARI) a(n) = valuation( n!, 4 ); /* Joerg Arndt, Mar 10 2013 */
(Python 3.10+)
def A090616(n): return (n-n.bit_count())>>1 # Chai Wah Wu, Jul 09 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Dec 06 2003
STATUS
approved