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A351915
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Number of polynomials of degree n over GF(2) in which the degrees of all distinct irreducible factors are distinct.
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0
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1, 2, 3, 6, 12, 24, 47, 94, 186, 372, 732, 1464, 2909, 5818, 11520, 23080, 45890, 91740, 182607, 365214, 727086, 1455764, 2900362, 5799012, 11570477, 23141098, 46148040, 92348504, 184258246, 368453148, 735743974, 1471456940, 2937243564, 5876474992, 11734526504
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of polynomials p in F_2[z] with p = p_1^e_1*...*p_k^e_k where each p_i is irreducible and deg(p_i) != deg(p_j) for all i != j.
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LINKS
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FORMULA
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G.f.: Product_{n>=1} (b(n)/(1-x^n) - b(n) +1) where b(n) = A001037(n).
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EXAMPLE
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a(2) = 3 because we have: x^2, (x+1)^2, x^2+x+1.
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MATHEMATICA
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nn = 30; b := Table[1/n Sum[MoebiusMu[d] 2^(n/d), {d, Divisors[n]}], {n, 1, nn}]; CoefficientList[ Series[Product[b[[i]]/(1 - x^i) - b[[i]] + 1, {i, 1, nn}], {x, 0, nn}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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