A048276 a(n) = number of squarefree numbers among C(n,k), k=0..n.

1, 2, 3, 4, 3, 6, 6, 8, 3, 2, 6, 12, 4, 10, 12, 14, 2, 6, 2, 8, 8, 10, 12, 24, 4, 4, 8, 2, 4, 12, 6, 12, 2, 4, 8, 8, 2, 8, 14, 12, 4, 12, 14, 26, 16, 8, 20, 42, 2, 2, 2, 4, 6, 18, 4, 6, 2, 6, 10, 22, 8, 26, 40, 8, 2, 4, 6, 8, 8, 16, 12, 18, 2, 8, 18, 4, 6, 14, 18, 34, 2, 2, 4, 6, 4, 10, 12, 16, 4

Offset

0,2

Comments

The only odd numbers are at n = 0, 2, 4, and 8. So this sequence is essentially twice A238337. - T. D. Noe, Mar 07 2014

Links

T. D. Noe, Table of n, a(n) for n = 0..5000

Formula

a(n) = n+1-A048277(n). - R. J. Mathar, Jan 18 2018

Example

If n=20, then C(20, k) is squarefree for k = 0,2,4,8,12,16,18,20, that is, for 8 cases of k, so a(20)=8.

Maple

A048276 := proc(n)
    local a, k ;
    a := 0 ;
    for k from 0 to n do
        if issqrfree(binomial(n, k)) then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
seq(A048276(n), n=0..40) ; # R. J. Mathar, Jan 18 2018

Mathematica

Table[Length[Select[Binomial[n, Range[0, n]], SquareFreeQ[#] &]], {n, 0, 100}]

Prog

(PARI) a(n) = sum(k=0, n, issquarefree(binomial(n, k))); \\ Michel Marcus, Dec 19 2013

Crossrefs

Cf. A005117, A046098, A048277, A238337.

Sequence in context: A341312 A347123 A318510 * A377499 A127463 A076618

Adjacent sequences: A048273 A048274 A048275 * A048277 A048278 A048279

Keyword

nonn

Author

Labos Elemer

Status

approved