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A037226
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phi(2n+1) / multiplicative order of 2 mod 2n+1.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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 (noe(AT)sspectra.com), 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
| T. D. Noe, Table of n, a(n) for n=0..10000
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FORMULA
| a(n) = Sum{d|2n+1} mu((2n+1)/d) A000374(d), the inverse Mobius transform of A000374 - T. D. Noe (noe(AT)sspectra.com), Aug 01 2003
A037226(n)=A037225(n)/A002326(n).
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CROSSREFS
| Cf. A000374 (number of irreducible factors of x^n - 1 over integers mod 2), A081844.
Cf. A006694 (cyclotomic cosets of 2 mod 2n+1).
Sequence in context: A025864 A070242 A202111 * A089641 A086995 A135230
Adjacent sequences: A037223 A037224 A037225 * A037227 A037228 A037229
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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