A245268 Sum of binomial(n,k) over squarefree k.

1, 3, 7, 14, 26, 48, 92, 184, 375, 758, 1497, 2884, 5461, 10286, 19507, 37584, 73866, 147987, 301075, 618794, 1278116, 2640993, 5439593, 11138764, 22640100, 45644797, 91293390, 181301470, 358024924, 704359427, 1383415456, 2718141072, 5351701032, 10570658330

Offset: 1

Author

Eric M. Schmidt, Jul 15 2014

Keywords

• nonn

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000
• J. E. Nymann and W. J. Leahey, On the probability that an integer chosen according to the binomial distribution be k-free, Rocky Mountain Journal of Mathematics 7 (1977), no. 4, 769-774.

Crossrefs

Cf. A013928, A060431, A245269.

Programs

Mathematica

a[n_] := Sum[Binomial[n, k], {k, Select[Range[n], SquareFreeQ]}]; Array[a, 34] (* Amiram Eldar, May 25 2025 *)

PARI

a(n) = sum(k=1, n, if (issquarefree(k), binomial(n,k), 0)); \\ Michel Marcus, Jul 16 2014

Sage

def A235268(n) : return sum(binomial(n,k) for k in range(1,n+1) if is_squarefree(k))

Formula

a(n) ~ 2^n/zeta(2). [Take p = 1/2 in Nymann and Leahey.]