A090616 Exponent of highest power of 4 dividing n!.

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

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Cf. A011371, A054861, A027868, A054896, A235127.

Sequence in context: A377028 A225559 A082479 * A186704 A067434 A336348

Adjacent sequences: A090613 A090614 A090615 * A090617 A090618 A090619

Keyword

nonn

Author

Henry Bottomley, Dec 06 2003

Status

approved