A294893 - OEIS

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A294893

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

6

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

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OFFSET

1,6

COMMENTS

Number of terms > 1 of A186891 that divide n.

LINKS

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

FORMULA

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

a(n) + A294894(n) = A000005(n).

a(n) = A294891(n) + A283991(n).

EXAMPLE

For n=25, with divisors [1, 5, 25], both B(5,x) and B(25,x) are irreducible, thus a(25)=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));

A294893(n) = sumdiv(n, d, A283991(d));

CROSSREFS

Cf. A186891, A283991, A294891, A294892, A294894.

Cf. also A294883.

Differs from A001221 for the first time at n=25.

Sequence in context: A354870 A050320 A333175 * A336570 A121382 A305150

Adjacent sequences: A294890 A294891 A294892 * A294894 A294895 A294896

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 10 2017

STATUS

approved