A294892 Number of proper divisors d of n such that either d=1 or Stern polynomial B(d,x) is reducible.

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

Offset: 1

Author

Antti Karttunen, Nov 10 2017

Keywords

• nonn

Examples

			For n=48, its proper divisors are [1, 2, 3, 4, 6, 8, 12, 16, 24]. After 1, the divisors 4, 6, 8, 12, 16 and 24 are not found in A186891, thus a(48) = 1+6 = 7.
For n=50, its proper divisors are [1, 2, 5, 10, 25]. After 1, only 10 is not found in A186891, thus a(50) = 1+1 = 2.
		

Links

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

Crossrefs

Cf. A186891, A283991, A294891, A294893, A294894.

Cf. also A294882, A294902.

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));
A294892(n) = sumdiv(n,d,(dA283991(d)));

Formula

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

a(n) + A294891(n) = A032741(n).

a(n) = A294894(n) + A283991(n) - 1.