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#16 by N. J. A. Sloane at Mon Jul 22 15:22:47 EDT 2024
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#15 by Amiram Eldar at Mon Jul 22 02:10:07 EDT 2024
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#14 by Amiram Eldar at Mon Jul 22 01:41:11 EDT 2024
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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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| 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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Cf. A001221, A001405, A034444, A034973, A056169, A056175.
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#13 by Amiram Eldar at Mon Jul 22 01:40:04 EDT 2024
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#12 by Alois P. Heinz at Fri Oct 27 20:54:55 EDT 2017
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#11 by Michel Marcus at Fri Oct 27 01:06:25 EDT 2017
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#10 by Michel Marcus at Fri Oct 27 01:06:19 EDT 2017
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| COMMENTS
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A prime divisor is unitary iff its exponent equals 1.
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| FORMULA
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A prime divisor is unitary iff its exponent equals 1.
a(n) = A034444(A001405(n)). - Michel Marcus, Oct 27 2017
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| STATUS
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proposed
editing
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#9 by Michael De Vlieger at Thu Oct 26 22:50:57 EDT 2017
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#8 by Michael De Vlieger at Thu Oct 26 22:50:45 EDT 2017
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| LINKS
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Michael De Vlieger, <a href="/A056173/b056173.txt">Table of n, a(n) for n = 1..10000</a>
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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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| STATUS
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approved
editing
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#7 by Susanna Cuyler at Mon Sep 04 19:23:55 EDT 2017
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