A090621 Exponent of highest power of 16 dividing n!.

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

Author

Henry Bottomley, Dec 06 2003

Keywords

• nonn

Examples

			a(10)=2 since 10! = 3628800 = 16^2 * 14175.
		

Crossrefs

Cf. A011371, A054861, A090616, A027868, A054896, A090617, A090618, A090619, A090620.

Programs

PARI

a(n) = valuation(n!, 16); \\ Michel Marcus, Jul 10 2022

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.