cp's OEIS Frontend

A304094 Number of Lucas numbers (A000204: 1, 3, 4, 7, 11, ... excluding 2) that divide n.

%I A304094 #17 Jul 23 2025 15:59:25
%S A304094 1,1,2,2,1,2,2,2,2,1,2,3,1,2,2,2,1,3,1,2,3,2,1,3,1,1,2,3,2,2,1,2,3,1,
%T A304094 2,4,1,1,2,2,1,3,1,3,2,1,2,3,2,1,2,2,1,3,2,3,2,2,1,3,1,1,3,2,1,3,1,2,
%U A304094 2,2,1,4,1,1,2,3,3,2,1,2,2,1,1,4,1,1,3,3,1,3,2,2,2,2,1,3,1,2,3,2,1,2,1,2,3
%N A304094 Number of Lucas numbers (A000204: 1, 3, 4, 7, 11, ... excluding 2) that divide n.
%H A304094 Antti Karttunen, <a href="/A304094/b304094.txt">Table of n, a(n) for n = 1..65537</a>
%F A304094 a(n) = A304092(n) - A059841(n).
%F A304094 a(n) = A304096(n) + A079978(n) + 1.
%F A304094 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A093540 = 1.962858... . - _Amiram Eldar_, Dec 31 2023
%o A304094 (PARI)
%o A304094 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 A304094 A304094(n) = sumdiv(n,d,isA000204(d));
%Y A304094 Cf. A000204, A093540, A304092, A304093, A304096.
%Y A304094 Cf. also A005086, A300837.
%K A304094 nonn
%O A304094 1,3
%A A304094 _Antti Karttunen_, May 13 2018