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

%I A294879 #10 Nov 10 2017 21:14:05
%S A294879 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,
%T A294879 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,
%U A294879 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
%N A294879 Number of proper divisors of n that are in Perrin sequence, A001608.
%H A294879 Antti Karttunen, <a href="/A294879/b294879.txt">Table of n, a(n) for n = 1..24914</a>
%F A294879 a(n) = Sum_{d|n, d<n} A294878(d).
%F A294879 a(n) = A294880(n) - A294878(n).
%e A294879 For n = 22, with proper divisors [1, 2, 11], only 2 is in A001608, thus a(22) = 1.
%e A294879 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.
%e A294879 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.
%o A294879 (PARI)
%o A294879 A001608(n) = if(n<0, 0, polsym(x^3-x-1, n)[n+1]);
%o A294879 A294878(n) = { my(k=1,v); while((v=A001608(k))<n,k++); (v==n); };
%o A294879 A294879(n) = sumdiv(n,d,(d<n)*A294878(d));
%Y A294879 Cf. A001608, A014981, A074788, A294878, A294880.
%Y A294879 Cf. also A293433, A293435.
%K A294879 nonn
%O A294879 1,6
%A A294879 _Antti Karttunen_, Nov 10 2017