A294882 Number of proper divisors of n that are not irreducible when their binary expansion is interpreted as polynomial over GF(2).

0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 3, 1, 3, 1, 4, 1, 1, 1, 5, 2, 1, 2, 3, 1, 5, 1, 4, 1, 2, 2, 6, 1, 1, 1, 6, 1, 4, 1, 3, 4, 2, 1, 7, 1, 3, 2, 3, 1, 5, 2, 5, 1, 2, 1, 9, 1, 1, 3, 5, 2, 4, 1, 4, 2, 5, 1, 9, 1, 1, 3, 3, 1, 4, 1, 8, 3, 1, 1, 8, 3, 2, 2, 5, 1, 9, 1, 4, 1, 1, 2, 9, 1, 3, 3, 6, 1, 5, 1, 5, 5

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..21845

Index entries for sequences related to polynomials in ring GF(2)[X]

Formula

a(n) = Sum_{d|n, d<n} (1-A091225(d)).

a(n) + A294881(n) = A032741(n).

For n > 1, a(n) = A294884(n) + A091225(n) - 1.

Prog

(PARI) A294882(n) = sumdiv(n, d, (d<n) * !polisirreducible(Mod(1, 2)*Pol(binary(d))));

Crossrefs

Cf. A032741, A091225, A294881, A294884.

Cf. also A234741, A234742, A294892.

Sequence in context: A239701 A303755 A321279 * A048220 A182593 A201167

Adjacent sequences: A294879 A294880 A294881 * A294883 A294884 A294885

Keyword

nonn

Author

Antti Karttunen, Nov 09 2017

Status

approved