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Sum of binomial(n,k) over squarefree k.
2

%I #24 Dec 07 2019 12:18:27

%S 1,3,7,14,26,48,92,184,375,758,1497,2884,5461,10286,19507,37584,73866,

%T 147987,301075,618794,1278116,2640993,5439593,11138764,22640100,

%U 45644797,91293390,181301470,358024924,704359427,1383415456,2718141072,5351701032,10570658330

%N Sum of binomial(n,k) over squarefree k.

%H Eric M. Schmidt, <a href="/A245268/b245268.txt">Table of n, a(n) for n = 1..1000</a>

%H J. E. Nymann and W. J. Leahey, <a href="http://dx.doi.org/10.1216/RMJ-1977-7-4-769">On the probability that an integer chosen according to the binomial distribution be k-free</a>, Rocky Mountain Journal of Mathematics 7 (1977), no. 4, 769-774.

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

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

%o (PARI) a(n) = sum(k=1, n, if (issquarefree(k), binomial(n,k), 0)); \\ _Michel Marcus_, Jul 16 2014

%Y Cf. A013928, A060431, A245269.

%K nonn

%O 1,2

%A _Eric M. Schmidt_, Jul 15 2014