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Search: id:A007839
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| A007839 |
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Number of polynomials of degree n over GF(2) in which the degrees of all irreducible factors are distinct. |
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+0
1
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| 1, 2, 1, 4, 7, 14, 28, 54, 111, 218, 436, 854, 1735, 3432, 6825, 13664, 27352, 54218, 108714, 216616, 432239, 864548, 1727408, 3441364, 6891458, 13756440, 27466896, 54922134, 109751871, 219035562, 438319568, 875529382
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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A. Knopfmacher and R. Warlimont, Distinct degree factorizations for polynomials over a finite field, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2235-2243.
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FORMULA
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G.f.: prod {m ge 1} (1 + pi(m) x^m), where pi(m) = A001037(m) = number of distinct irreducible polynomials of degree m.
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EXAMPLE
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a(3)=4 from x^3+x+1, x^3+x^2+1, x(x^2+x+1), (x+1)(x^2+x+1).
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CROSSREFS
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Sequence in context: A123360 A072015 A123242 this_sequence A045625 A001933 A038557
Adjacent sequences: A007836 A007837 A007838 this_sequence A007840 A007841 A007842
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Arnold Knopfmacher [ ARNOLDK(AT)gauss.cam.wits.ac.za ]
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net).
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