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

0,11

Links

Table of n, a(n) for n=0..83.

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

Crossrefs

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

Sequence in context: A120450 A127238 A072114 * A173711 A236678 A029378

Adjacent sequences: A090618 A090619 A090620 * A090622 A090623 A090624

Keyword

nonn

Author

Henry Bottomley, Dec 06 2003

Status

approved