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A245268
Sum of binomial(n,k) over squarefree k.
2
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
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
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Jul 15 2014
STATUS
approved