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A294880 Number of divisors of n that are in Perrin sequence, A001608.

%I A294880 #12 Jan 01 2024 08:00:25
%S A294880 0,1,1,1,1,2,1,1,1,3,0,3,0,2,2,1,1,2,0,3,2,2,0,3,1,1,1,2,1,4,0,1,1,2,
%T A294880 2,3,0,1,2,3,0,3,0,2,2,1,0,3,1,3,3,1,0,2,1,2,1,2,0,5,0,1,2,1,1,3,0,3,
%U A294880 1,4,0,3,0,1,2,1,1,3,0,3,1,1,0,4,2,1,2,2,0,5,1,1,1,1,1,3,0,2,1,3,0,4,0,1,3
%N A294880 Number of divisors of n that are in Perrin sequence, A001608.
%H A294880 Antti Karttunen, <a href="/A294880/b294880.txt">Table of n, a(n) for n = 1..24914</a>
%F A294880 a(n) = Sum_{d|n} A294878(d).
%F A294880 a(n) = A294879(n) + A294878(n).
%F A294880 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = -1/5 + Sum_{n>=3} 1/A001608(n) = 1.603595519775230150708... . - _Amiram Eldar_, Jan 01 2024
%e A294880 For n = 22, with divisors [1, 2, 11, 22], both 2 and 22 are in A001608, thus a(22) = 2.
%e A294880 For n = 644, with divisors [1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644], 2, 7 and 644 are in A001608, thus a(644) = 3.
%t A294880 With[{s = LinearRecurrence[{0, 1, 1}, {3, 2, 5}, 15]}, Table[DivisorSum[n, 1 &, MemberQ[s, #] &], {n, 1, s[[-1]]}]] (* _Amiram Eldar_, Jan 01 2024 *)
%o A294880 (PARI)
%o A294880 A001608(n) = if(n<0, 0, polsym(x^3-x-1, n)[n+1]);
%o A294880 A294878(n) = { my(k=1,v); while((v=A001608(k))<n,k++); (v==n); };
%o A294880 A294880(n) = sumdiv(n,d,A294878(d));
%Y A294880 Cf. A001608, A014981, A074788, A294878, A294879.
%Y A294880 Cf. also A005086, A293431.
%K A294880 nonn
%O A294880 1,6
%A A294880 _Antti Karttunen_, Nov 10 2017