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A048276 a(n) = number of squarefree numbers among C(n,k), k=0..n. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A074792 A321168 A318510 * A127463 A076618 A116550

Adjacent sequences:  A048273 A048274 A048275 * A048277 A048278 A048279

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified September 17 11:15 EDT 2019. Contains 327129 sequences. (Running on oeis4.)