A294884 Number of divisors of n that are not irreducible when their binary expansion is interpreted as polynomial over GF(2).

1, 1, 1, 2, 2, 2, 1, 3, 2, 3, 1, 4, 1, 2, 3, 4, 2, 4, 1, 5, 2, 2, 2, 6, 2, 2, 3, 4, 2, 6, 1, 5, 2, 3, 3, 7, 1, 2, 2, 7, 1, 5, 2, 4, 5, 3, 1, 8, 2, 4, 3, 4, 2, 6, 2, 6, 2, 3, 1, 10, 1, 2, 4, 6, 3, 5, 1, 5, 3, 6, 2, 10, 1, 2, 4, 4, 2, 5, 2, 9, 4, 2, 2, 9, 4, 3, 2, 6, 2, 10, 1, 5, 2, 2, 3, 10, 1, 4, 4, 7, 2, 6, 1, 6, 6

Offset

1,4

Comments

One more than the number of terms of A091242 that divide n: +1 is for divisor 1, which is also included in the count.

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} (1-A091225(d)).

a(n) + A294883(n) = A000005(n).

For n > 1, a(n) = 1 + A294882(n) - A091225(n).

Prog

(PARI) A294884(n) = sumdiv(n, d, !polisirreducible(Mod(1, 2)*Pol(binary(d))));

Crossrefs

Cf. A000005, A091225, A091242, A294882, A294883.

Cf. also A234741, A234742, A294894.

Sequence in context: A349273 A091222 A316506 * A275024 A325121 A064659

Adjacent sequences: A294881 A294882 A294883 * A294885 A294886 A294887

Keyword

nonn

Author

Antti Karttunen, Nov 09 2017

Status

approved