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Search: id:A056651
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| A056651 |
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Numbers n such that binomial[n,Floor[n/2]] has no non-unitary square divisors: all of their square divisors are unitary ones. |
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+0
2
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 31, 32, 35, 36, 37, 39, 40, 41, 43, 47, 48, 49, 55, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 75, 79, 80, 95, 96, 97, 111, 129, 130, 131, 132, 133, 143, 144, 151, 161, 163, 167, 191, 192, 193
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This property is weaker than "square-freedom", but shows how central binomial coefficients are "poor of squares".
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..128 (no others < 10^8)
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EXAMPLE
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n=223, x=binomial[223,111] has 35 prime divisors. 33 arises at power 1. Only 2 and 13 has powers 2>1. So square divisors of x are {1,4,169,676}={s}. All of them are also unitary divisors since GCD[s,x/s]=1 holds for them.
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CROSSREFS
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A046098, A056175.
Cf. A110495
Sequence in context: A023807 A023755 A114886 this_sequence A022772 A004440 A026495
Adjacent sequences: A056648 A056649 A056650 this_sequence A056652 A056653 A056654
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Aug 09 2000
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