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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
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved