login
A294879
Number of proper divisors of n that are in Perrin sequence, A001608.
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 10 2017
STATUS
approved