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A056649
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Number of non-unitary square divisors of central binomial coefficient.
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0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 4, 6, 2, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 6, 8, 0, 0, 0, 4, 4, 6, 2, 2, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 4, 4, 0, 0, 4, 8, 2, 3, 6, 8, 4, 8, 2, 2, 4, 4, 8, 8, 0, 0, 0, 4, 2, 4, 3, 4, 2, 3, 4
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OFFSET
| 1,26
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FORMULA
| a(n)=A056061(n)-2^r, where r is the number of prime factors in the largest unitary square(or square root) divisor of central binomial coefficient: r=A001221[A000188(A001405(n))/A055229(A001405(n))]
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EXAMPLE
| n=28, binomial[28,14]=2.2.2.3.3.3.5.5.17.19.23. Its has 384 divisors of which 8 are also square numbers: {1,4,9,25,36,100,225,900}and Only {4,9,36,100,225,900} are not unitary divisors. Thus a(28)=8-2=6. Observe large values (e.g. 223), where a(n)=0.
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CROSSREFS
| A000188, A001405, A055229, A056056, A056057, A056059, A056061, A008833, A034444.
Sequence in context: A077069 A080413 A004517 * A075242 A161489 A050975
Adjacent sequences: A056646 A056647 A056648 * A056650 A056651 A056652
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Aug 09 2000
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