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

1,8

Links

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

Formula

a(n) = Sum_{d|n, d<n} (1-A283991(d)).

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

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

Example

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.

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));
A294892(n) = sumdiv(n, d, (d<n)*(0==A283991(d)));

Crossrefs

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

Cf. also A294882, A294902.

Sequence in context: A331024 A115561 A115622 * A371211 A108886 A140886

Adjacent sequences: A294889 A294890 A294891 * A294893 A294894 A294895

Keyword

nonn

Author

Antti Karttunen, Nov 10 2017

Status

approved