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A056173
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Number of unitary prime divisors of central binomial coefficient C(n, floor(n/2)) (A001405).
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4
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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, 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, 11, 13, 12, 13, 12, 12, 12, 14, 13, 13, 13, 13, 13, 11, 11, 14, 13, 12, 12, 14, 14, 13, 13, 13
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OFFSET
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1,4
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COMMENTS
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A prime divisor is unitary iff its exponent equals 1.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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Array[Function[k, Count[FactorInteger[k][[All, 1]], _?(CoprimeQ[#, k/#] &)]]@ Binomial[#, Floor[#/2]] &, 87] (* Michael De Vlieger, Oct 26 2017 *)
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PROG
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(PARI) a(n) = vecsum(apply(x -> if(x > 1, 0, 1), factor(binomial(n, n\2))[, 2])); \\ Amiram Eldar, Jul 22 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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