A279515 Number of 0's in the binary expansion of the least common multiple of the first n integers.

0, 0, 1, 1, 2, 2, 2, 5, 6, 6, 6, 9, 9, 7, 7, 7, 8, 12, 12, 16, 16, 16, 16, 19, 19, 14, 14, 19, 19, 25, 25, 25, 26, 26, 26, 26, 26, 25, 25, 25, 25, 33, 33, 32, 32, 32, 32, 29, 29, 32, 32, 32, 32, 35, 35, 35, 35, 35, 35, 46, 46, 45

Offset

0,5

Links

Indranil Ghosh, Table of n, a(n) for n = 0..10000

Example

For n = 10, the LCM of all the numbers from 1 to 10 is 2520 = 100111011000_2, which has a total of 6 0's, so a(10) = 6.

Mathematica

Map[DigitCount[#, 2, 0] &, {1}~Join~Table[LCM @@ Range@ n, {n, 61}]] (* Michael De Vlieger, Dec 16 2016 *)

Prog

(Python)
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a
def lcm(a, b):
    return a * b // gcd(a, b)
def c(*ar):
    return reduce(lcm, ar)
def a(n):
    if n==0:
        return 0
    x=bin(c(*range(1, n+1)))[2:]
    return x.count("0")
for i in range(0, 10001):
    print str(i)+" "+str(a(i))
(PARI) a(n) = my(lcmn = lcm(vector(n, k, k))); #binary(lcmn) - hammingweight(lcmn); \\ Michel Marcus, Dec 23 2016

Crossrefs

Cf. A003418, A279506.

Sequence in context: A097006 A033306 A136347 * A260338 A023569 A263373

Adjacent sequences: A279512 A279513 A279514 * A279516 A279517 A279518

Keyword

nonn,base

Author

Indranil Ghosh, Dec 13 2016

Status

approved