

A056173


Number of unitary prime divisors of central binomial coefficient C(n, floor(n/2)) (A001405).


4



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

1,4


COMMENTS

A prime divisor is unitary iff its exponent equals 1.


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A034444(A001405(n)).  Michel Marcus, Oct 27 2017


EXAMPLE

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.


MATHEMATICA

Array[Function[k, Count[FactorInteger[k][[All, 1]], _?(CoprimeQ[#, k/#] &)]]@ Binomial[#, Floor[#/2]] &, 87] (* Michael De Vlieger, Oct 26 2017 *)


CROSSREFS

Cf. A001221, A001405, A034444, A034973, A056175.
Sequence in context: A046923 A184703 A309287 * A216817 A263765 A270073
Adjacent sequences: A056170 A056171 A056172 * A056174 A056175 A056176


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 27 2000


STATUS

approved



