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Search: id:A056175
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| A056175 |
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Number of non-unitary prime divisors of the central binomial coefficient C(n, floor(n/2)) (A001405). |
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6
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| 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 3, 3, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 0, 1, 1, 1, 2, 2, 3, 3, 1, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2
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OFFSET
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1,10
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COMMENT
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Nonunitary prime divisors are the prime divisors of largest square dividing the number: a(n)=A001221[A000188[A001405[n]]]=A001221[A056057[n]]
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FORMULA
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A prime divisor is not unitary iff its exponent exceeds 1.
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EXAMPLE
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n=10, binomial[10, 5]=252=2.2.3.3.7 has 3 prime divisors of which only 1, p=7 is unitary, while 2, 3 are not. So a(10)=2. n=256, binomial[256, 128] also has only 2 prime divisors, 3 and 13, whose exponents are >1, 4 or 2 resp., thus a(256)=2.
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CROSSREFS
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Cf. A001405, A001221, A034444, A034973, A039593, A056057, A056173.
Sequence in context: A125184 A091430 A059282 this_sequence A105241 A134541 A070200
Adjacent sequences: A056172 A056173 A056174 this_sequence A056176 A056177 A056178
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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), Jul 27 2000
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