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

1,2

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.

Formula

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

Prog

(Sage) def A235268(n) : return sum(binomial(n, k) for k in range(1, n+1) if is_squarefree(k))
(PARI) a(n) = sum(k=1, n, if (issquarefree(k), binomial(n, k), 0)); \\ Michel Marcus, Jul 16 2014

Crossrefs

Cf. A013928, A060431, A245269.

Sequence in context: A317779 A099854 A054355 * A117071 A019459 A276024

Adjacent sequences: A245265 A245266 A245267 * A245269 A245270 A245271

Keyword

nonn

Author

Eric M. Schmidt, Jul 15 2014

Status

approved