

A107067


Number of polynomials with coefficients in {0,1} and which divide x^n1.


3



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

1,2


COMMENTS

From Robert Israel, May 22 2017:
Each of these polynomials is a product of distinct cyclotomic polynomials C_k(x) for k > 1 dividing n.
a(n) <= 2^(A000005(n)1).
If n is prime then a(n) = 2. (End)


LINKS

Robert Israel, Table of n, a(n) for n = 1..719(first 359 terms from Antti Karttunen)


MAPLE

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:
map(f, [$1..100]); # Robert Israel, May 22 2017


PROG

(PARI) for(n=1, 100, m=0; p=x^n1; 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


CROSSREFS

Cf. A107336, A107748.
Sequence in context: A278237 A328707 A067824 * A331580 A320389 A046801
Adjacent sequences: A107064 A107065 A107066 * A107068 A107069 A107070


KEYWORD

nonn


AUTHOR

Ralf Stephan, following a suggestion from Max Alekseyev, Jun 11 2005


EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 15 2006
Data section further extended and bfile computed with Jamke's PARIprogram by Antti Karttunen, May 22 2017


STATUS

approved



