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

Author

Antti Karttunen, Nov 10 2017

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Cf. also A294881, A294901.

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

Programs

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,(dA283991(d));

Formula

a(n) = Sum_{d|n, dA283991(d).

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

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