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A090621
Exponent of highest power of 16 dividing n!.
2
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19
OFFSET
0,11
FORMULA
a(n) = A090622(n, 16) = floor(A011371(n)/4) = floor(A090616(n)/2) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/4). Almost n/4.
EXAMPLE
a(10)=2 since 10! = 3628800 = 16^2 * 14175.
PROG
(Python 3.10+)
def A090621(n): return (n-n.bit_count())>>2 # Chai Wah Wu, Jul 09 2022
(PARI) a(n) = valuation(n!, 16); \\ Michel Marcus, Jul 10 2022
KEYWORD
nonn
AUTHOR
Henry Bottomley, Dec 06 2003
STATUS
approved