A090617 Exponent of highest power of 8 dividing n!.

0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24

Offset

0,9

Links

Table of n, a(n) for n=0..79.

Formula

a(n) = A090622(n, 8) = floor(A011371(n)/3) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/3).

a(n) = A244413(n!) . - R. J. Mathar, Jul 08 2021

Example

a(8)=2 since 8! = 40320 = 8^2 * 630.

Mathematica

Table[IntegerExponent[n!, 8], {n, 0, 80}] (* Harvey P. Dale, Mar 21 2013 *)

Prog

(Python 3.10+)
def A090617(n): return (n-bin(n).count('1'))//3 # Chai Wah Wu, Jul 09 2022
(PARI) a(n) = valuation(n!, 8); \\ Michel Marcus, Jul 10 2022

Crossrefs

Cf. A011371, A054861, A090616, A027868, A054896.

Sequence in context: A132011 A363822 A054893 * A053693 A330324 A341132

Adjacent sequences: A090614 A090615 A090616 * A090618 A090619 A090620

Keyword

nonn

Author

Henry Bottomley, Dec 06 2003

Status

approved