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A279515 Number of 0's in the binary expansion of the least common multiple of the first n integers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 26 07:21 EDT 2017. Contains 284111 sequences.