A245269 Sum of binomial(n,k) over cubefree k.

1, 3, 7, 15, 31, 63, 127, 254, 502, 978, 1882, 3600, 6904, 13380, 26332, 52664, 106744, 218232, 447736, 917760, 1873312, 3799920, 7653136, 15306272, 30429856, 60234528, 118956831, 234885092, 464595690, 921868388, 1836393687, 3672648928, 7369572624, 14821243232

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(3). [Take p = 1/2 in Nymann and Leahey.]

Mathematica

cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; a[n_] := Sum[Binomial[n, k], {k, Select[Range[n], cubeFreeQ]}]; Array[a, 34] (* Amiram Eldar, May 25 2025 *)

Prog

(SageMath) def A245269(n) : return sum(binomial(n, k) for k in range(1, n+1) if all(m <= 2 for (p, m) in factor(k)))

Crossrefs

Cf. A013928, A060431, A245268.

Sequence in context: A283091 A277716 A116082 * A043747 A105754 A116690

Adjacent sequences: A245266 A245267 A245268 * A245270 A245271 A245272

Keyword

nonn

Author

Eric M. Schmidt, Jul 15 2014

Status

approved