A294891 Number of proper divisors d of n such that Stern polynomial B(d,x) is irreducible.

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 1, 2, 0, 3, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 3, 0, 2, 2, 2, 0, 2, 1, 3, 2, 2, 0, 2, 2, 2, 2, 2, 0, 3, 0, 2, 2, 1, 2, 3, 0, 2, 2, 3, 0, 2, 0, 2, 3, 2, 2, 3, 0, 2, 1, 2, 0, 3, 2, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 2, 0, 2, 2, 3, 0, 3, 0, 2, 3

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..22001

Formula

a(n) = Sum_{d|n, d<n} A283991(d).

a(n) + A294892(n) = A032741(n).

a(n) = A294893(n) - A283991(n).

Example

For n=50, with proper divisors [1, 2, 5, 10, 25], 2, 5, and 25 are larger than one and included in A186891, thus a(50) = 3.

Prog

(PARI)
ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));
A283991(n) = polisirreducible(ps(n));
A294891(n) = sumdiv(n, d, (d<n)*A283991(d));

Crossrefs

Cf. A186891, A283991, A294892, A294893, A294894.

Cf. also A294881, A294901.

Differs from A087624 for the first time at n=50.

Sequence in context: A333750 A072670 A087624 * A294879 A085122 A329867

Adjacent sequences: A294888 A294889 A294890 * A294892 A294893 A294894

Keyword

nonn

Author

Antti Karttunen, Nov 10 2017

Status

approved