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%I #16 Jul 22 2024 15:22:47
%S 0,1,1,2,2,1,2,3,2,1,4,3,3,3,3,4,5,4,5,4,5,5,6,5,4,4,3,3,5,5,6,7,7,6,
%T 8,7,7,7,9,8,9,9,9,9,6,6,8,7,7,7,7,7,8,8,11,11,12,12,11,11,11,11,10,
%U 11,13,12,13,12,12,12,14,13,13,13,13,13,11,11,14,13,12,12,14,14,13,13,13
%N Number of unitary prime divisors of central binomial coefficient C(n, floor(n/2)) (A001405).
%C A prime divisor is unitary iff its exponent equals 1.
%H Michael De Vlieger, <a href="/A056173/b056173.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A056169(A001405(n)). - _Michel Marcus_, Oct 27 2017 [corrected by _Amiram Eldar_, Jul 22 2024]
%e For n = 10: binomial(10,5) = 252 = 2*2*3*3*7 has 3 prime factors of which only one, p = 7, is unitary. So a(10) = 1.
%t Array[Function[k, Count[FactorInteger[k][[All, 1]], _?(CoprimeQ[#, k/#] &)]]@ Binomial[#, Floor[#/2]] &, 87] (* _Michael De Vlieger_, Oct 26 2017 *)
%o (PARI) a(n) = vecsum(apply(x -> if(x > 1, 0, 1), factor(binomial(n, n\2))[,2])); \\ _Amiram Eldar_, Jul 22 2024
%Y Cf. A001221, A001405, A034973, A056169, A056175.
%K nonn,changed
%O 1,4
%A _Labos Elemer_, Jul 27 2000
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