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A037226
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a(n) = phi(2n+1) / multiplicative order of 2 mod 2n+1.
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7
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1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 6, 2, 2, 1, 2, 2, 3, 2, 2, 2, 4, 1, 2, 2, 1, 1, 6, 4, 1, 2, 2, 8, 2, 2, 2, 1, 1, 8, 2, 8, 6, 6, 2, 2, 2, 1, 2, 4, 1, 3, 2, 4, 2, 6, 4, 1, 4, 1, 18, 6, 1, 6, 2, 2, 1, 2, 2, 4, 2, 1, 10, 4, 6, 3, 2, 4
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OFFSET
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0,4
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COMMENTS
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Number of primitive irreducible factors of x^(2n+1) - 1 over integers mod 2. There are no primitive irreducible factors for x^(2n)-1 because it always has the same factors as x^n-1. Considering that A000374 also counts the cycles in the map f(x) = 2x mod n, a(n) is also the number of primitive cycles of that mapping. - T. D. Noe, Aug 01 2003
Equals number of irreducible factors of the cyclotomic polynomial Phi(2n+1,x) over Z/2Z. All factors have the same degree. - T. D. Noe, Mar 01 2008
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := EulerPhi[2n+1]/MultiplicativeOrder[2, 2n+1]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 10 2015 *)
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PROG
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CROSSREFS
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Cf. A000374 (number of irreducible factors of x^n - 1 over integers mod 2), A081844.
Cf. A006694 (cyclotomic cosets of 2 mod 2n+1).
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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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