A078565 Number of zeros in the binary expansion of n!.

0, 0, 1, 1, 3, 3, 6, 7, 10, 13, 11, 19, 17, 21, 25, 23, 27, 27, 30, 40, 40, 41, 42, 44, 51, 54, 54, 56, 56, 63, 60, 71, 76, 77, 77, 77, 88, 86, 90, 90, 97, 99, 106, 105, 107, 117, 115, 117, 114, 122, 126, 130, 138, 138, 151, 144, 146, 157, 160, 158, 160, 176

Offset: 0

Author

Jose R. Brox (tautocrona(AT)terra.es), Jan 26 2003

Keywords

• nonn
• base

Examples

			a(4) = 3 because 4! = 24_10 = 11000_2 and it has 3 zero digits.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A072831, A079584.

Programs

Mathematica

Table[Count[IntegerDigits[n!, 2], 0], {n, 0, 100}] (* T. D. Noe, Apr 10 2012 *)
DigitCount[Range[0,70]!,2,0] (* Harvey P. Dale, Mar 11 2019 *)

PARI

for(n=1,300,b=binary(n!); print1(sum(k=1,length(b),if(b[k],0,1))","))

Python

import math
def a(n):
    return bin(math.factorial(n))[2:].count("0")
# Indranil Ghosh, Dec 23 2016

Formula

a(n) = A072831(n) - A079584(n). - Michel Marcus, Dec 23 2016