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A304093 a(n) is the number of the proper divisors of n that are Lucas numbers (A000204, with 2 excluded).

%I A304093 #10 Jul 05 2025 11:25:10
%S A304093 0,1,1,1,1,2,1,2,2,1,1,3,1,2,2,2,1,2,1,2,3,2,1,3,1,1,2,3,1,2,1,2,3,1,
%T A304093 2,4,1,1,2,2,1,3,1,3,2,1,1,3,2,1,2,2,1,3,2,3,2,2,1,3,1,1,3,2,1,3,1,2,
%U A304093 2,2,1,4,1,1,2,2,3,2,1,2,2,1,1,4,1,1,3,3,1,3,2,2,2,2,1,3,1,2,3,2,1,2,1,2,3
%N A304093 a(n) is the number of the proper divisors of n that are Lucas numbers (A000204, with 2 excluded).
%H A304093 Antti Karttunen, <a href="/A304093/b304093.txt">Table of n, a(n) for n = 1..65537</a>
%F A304093 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A093540. - _Amiram Eldar_, Jul 05 2025
%o A304093 (PARI)
%o A304093 isA000204(n) = { my(u1=1,u2=3,old_u1); if(n<=2,(n%2),while(n>u2,old_u1=u1;u1=u2;u2=old_u1+u2);(u2==n)); };
%o A304093 A304093(n) = sumdiv(n,d,(d<n)*isA000204(d));
%Y A304093 Cf. A000204, A093540, A304091, A304094, A304095.
%Y A304093 Cf. also A293435, A300836.
%K A304093 nonn
%O A304093 1,6
%A A304093 _Antti Karttunen_, May 13 2018