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A245269
Sum of binomial(n,k) over cubefree k.
2
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
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.]
PROG
(Sage) 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
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Jul 15 2014
STATUS
approved