A294879 Number of proper divisors of n that are in Perrin sequence, A001608.

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 3, 2, 1, 0, 3, 1, 1, 1, 2, 0, 4, 0, 1, 1, 2, 2, 3, 0, 1, 1, 3, 0, 3, 0, 2, 2, 1, 0, 3, 1, 3, 2, 1, 0, 2, 1, 2, 1, 2, 0, 5, 0, 1, 2, 1, 1, 3, 0, 2, 1, 4, 0, 3, 0, 1, 2, 1, 1, 3, 0, 3, 1, 1, 0, 4, 2, 1, 2, 2, 0, 4, 1, 1, 1, 1, 1, 3, 0, 2, 1, 3, 0, 4, 0, 1, 3, 1, 0, 3, 0, 4, 1, 2, 0, 2, 1, 2, 2, 1, 2, 5, 0

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..24914

Formula

a(n) = Sum_{d|n, d<n} A294878(d).

a(n) = A294880(n) - A294878(n).

Example

For n = 22, with proper divisors [1, 2, 11], only 2 is in A001608, thus a(22) = 1.
For n = 121, with proper divisors [1, 11], neither of them is in A001608, thus a(121) = 0. Note that this is the first zero not in A008578.
For n = 644, with proper divisors [1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644], both 2 and 7 are in A001608, thus a(644) = 2.

Prog

(PARI)
A001608(n) = if(n<0, 0, polsym(x^3-x-1, n)[n+1]);
A294878(n) = { my(k=1, v); while((v=A001608(k))<n, k++); (v==n); };
A294879(n) = sumdiv(n, d, (d<n)*A294878(d));

Crossrefs

Cf. A001608, A014981, A074788, A294878, A294880.

Cf. also A293433, A293435.

Sequence in context: A072670 A087624 A294891 * A085122 A329867 A342652

Adjacent sequences: A294876 A294877 A294878 * A294880 A294881 A294882

Keyword

nonn

Author

Antti Karttunen, Nov 10 2017

Status

approved