A279506 Total number of 1's in the binary expansion of A003418.

1, 1, 1, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 21, 21, 18, 18, 17, 17, 22, 22, 22, 22, 22, 22, 28, 28, 28, 28, 25, 25, 32, 32, 32, 32, 40, 40, 40, 40

Offset

0,4

Links

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

Formula

a(n) = A000120(A003418(n)). - Michel Marcus, Dec 23 2016

Example

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

Mathematica

Map[DigitCount[#, 2, 1] &, FoldList[LCM, 1, Range@ 50]] (* Michael De Vlieger, Dec 13 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 1
    x=bin(c(*range(1, n+1)))[2:]
    return x.count("1")
for i in range(0, 10001):
    print str(i)+" "+str(a(i))
(PARI) a(n) = hammingweight(lcm(vector(n, k, k))); \\ Michel Marcus, Dec 14 2016

Crossrefs

Cf. A000120, A003418.

Sequence in context: A076222 A177692 A098667 * A105678 A309195 A367026

Adjacent sequences: A279503 A279504 A279505 * A279507 A279508 A279509

Keyword

nonn,base

Author

Indranil Ghosh, Dec 13 2016

Status

approved