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Search: id:A089789
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| A089789 |
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Number of irreducible factors of Gauss polynomials. |
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+0
2
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| 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 1, 0, 0, 3, 3, 4, 3, 3, 0, 0, 1, 3, 3, 3, 3, 1, 0, 0, 3, 3, 5, 4, 5, 3, 3, 0, 0, 2, 4, 4, 5, 5, 4, 4, 2, 0, 0, 3, 4, 6, 5, 7, 5, 6, 4, 3, 0, 0, 1, 3, 4, 5, 5, 5, 5, 4, 3, 1, 0, 0, 5, 5, 7, 7, 9, 7, 9, 7, 7, 5, 5, 0, 0, 1, 5, 5, 6, 7, 7, 7, 7, 6, 5, 5, 1, 0
(list; table; graph; listen)
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OFFSET
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0,12
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COMMENT
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T(n,k) is the number of irreducible factors of the (separable) polynomial [n]!/([k]![n-k]!). Here [n]! denotes the product of the first n quantum integers, the n-th quantum integer being defined as (1-q^n)/(1-q).
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FORMULA
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T(n, k)=T(n-1, k-1)+d(n)-d(k), where d(n) is the number of divisors of n.
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EXAMPLE
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T(8,3) equals the number of irreducible factors of (1-q^8)(1-q^7)(1-q^6)/((1-q^3)(1-q^2)(1-q)), which is a product of 5 cyclotomic polynomials in q, namely the 2nd, 4th, 6th, 7th and 8th. Thus T(8,3)=5.
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CROSSREFS
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Sequence in context: A123186 A127323 A132896 this_sequence A004541 A037864 A034852
Adjacent sequences: A089786 A089787 A089788 this_sequence A089790 A089791 A089792
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Boddington (psb(AT)maths.warwick.ac.uk), Jan 09 2004
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