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A107067
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Number of polynomials with coefficients in {0,1} and which divide x^n - 1.
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3
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1, 2, 2, 4, 2, 6, 2, 8, 4, 6, 2, 17, 2, 6, 6, 16, 2, 18, 2, 17, 6, 6, 2, 48, 4, 6, 8, 17, 2, 36, 2, 32, 6, 6, 6, 69, 2, 6, 6, 47, 2, 36, 2, 17, 17, 6, 2, 136, 4, 18, 6, 17, 2, 54, 6, 47, 6, 6, 2, 176, 2, 6, 17, 64, 6, 36, 2, 17, 6, 36, 2, 257, 2, 6, 18, 17, 6, 36, 2, 131, 16, 6, 2, 177, 6, 6, 6, 47, 2, 183, 6, 17, 6, 6, 6, 389, 2, 18, 17, 70, 2, 36, 2, 47, 35
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OFFSET
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1,2
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COMMENTS
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Each of these polynomials is a product of distinct cyclotomic polynomials C_k(x) for k > 1 dividing n.
If n is prime then a(n) = 2. (End)
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LINKS
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MAPLE
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f:= proc(n) local t, C, x, S;
C:= map(m -> numtheory:-cyclotomic(m, x), numtheory:-divisors(n) minus {1});
t:= 0:
S:= combinat:-subsets(C);
while not S[finished] do
if {coeffs(expand(convert(S[nextvalue](), `*`)), x)} = {1} then
t:= t+1;
fi
od;
t
end proc:
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MATHEMATICA
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a[n_] := Module[{c, s},
c = Cyclotomic[#, x]& /@ Rest@Divisors[n];
s = CoefficientList[#, x]& /@ (Times @@@ Subsets[c]);
Select[s, AllTrue[#, # == 0 || # == 1&]&] // Length];
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PROG
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(PARI) for(n=1, 100, m=0; p=x^n-1; nE=numdiv(n); P=factor(p); E=P[, 2]; P=P[, 1]; forvec(v=vector(nE, i, [0, E[i]]), divp=prod(k=1, nE, P[k]^v[k]); m++; for(j=0, poldegree(divp), divpcof=polcoeff(divp, j); if(divpcof<0 || divpcof>1, m--; break))); print1(m, ", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 15 2006
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 15 2006
Data section further extended and b-file computed with Jamke's PARI-program by Antti Karttunen, May 22 2017
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STATUS
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approved
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