This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A304091 #12 Jul 05 2025 11:25:33
%S A304091 0,1,1,2,1,3,1,3,2,2,1,4,1,3,2,3,1,3,1,3,3,3,1,4,1,2,2,4,1,3,1,3,3,2,
%T A304091 2,5,1,2,2,3,1,4,1,4,2,2,1,4,2,2,2,3,1,4,2,4,2,3,1,4,1,2,3,3,1,4,1,3,
%U A304091 2,3,1,5,1,2,2,3,3,3,1,3,2,2,1,5,1,2,3,4,1,4,2,3,2,3,1,4,1,3,3,3,1,3,1,3,3
%N A304091 a(n) is the number of the proper divisors of n that are Lucas numbers (A000032, with 2 included).
%H A304091 Antti Karttunen, <a href="/A304091/b304091.txt">Table of n, a(n) for n = 1..65537</a>
%F A304091 a(n) = Sum_{d|n, d<n} A102460(d).
%F A304091 a(n) = A304092(n) - A102460(n).
%F A304091 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2 + A093540 = 2.462858... . - _Amiram Eldar_, Jul 05 2025
%o A304091 (PARI)
%o A304091 A102460(n) = { my(u1=1,u2=3,old_u1); if(n<=2,sign(n),while(n>u2,old_u1=u1;u1=u2;u2=old_u1+u2);(u2==n)); };
%o A304091 A304091(n) = sumdiv(n,d,(d<n)*A102460(d));
%Y A304091 Cf. A000032, A093540, A102460, A304092, A304093.
%Y A304091 Cf. also A293435, A300836.
%K A304091 nonn
%O A304091 1,4
%A A304091 _Antti Karttunen_, May 13 2018