cp's OEIS Frontend

A304092 Number of Lucas numbers (A000032: 2, 1, 3, 4, 7, 11, ...) dividing n.

%I A304092 #15 Dec 31 2023 06:22:59
%S A304092 1,2,2,3,1,3,2,3,2,2,2,4,1,3,2,3,1,4,1,3,3,3,1,4,1,2,2,4,2,3,1,3,3,2,
%T A304092 2,5,1,2,2,3,1,4,1,4,2,2,2,4,2,2,2,3,1,4,2,4,2,3,1,4,1,2,3,3,1,4,1,3,
%U A304092 2,3,1,5,1,2,2,4,3,3,1,3,2,2,1,5,1,2,3,4,1,4,2,3,2,3,1,4,1,3,3,3,1,3,1,3,3
%N A304092 Number of Lucas numbers (A000032: 2, 1, 3, 4, 7, 11, ...) dividing n.
%H A304092 Antti Karttunen, <a href="/A304092/b304092.txt">Table of n, a(n) for n = 1..65537</a>
%F A304092 a(n) = Sum_{d|n} A102460(d).
%F A304092 a(n) = A304091(n) + A102460(n).
%F A304092 a(n) = A304094(n) + A059841(n) = A304096(n) + A059841(n) + A079978(n) + 1.
%F A304092 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A093540 + 1/2 = 2.462858... . - _Amiram Eldar_, Dec 31 2023
%t A304092 Module[{nn=11,luc},luc=LucasL[Range[0,nn]];Table[Count[n/luc,_?IntegerQ],{n,Max[luc]}]] (* _Harvey P. Dale_, Jul 01 2023 *)
%o A304092 (PARI)
%o A304092 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 A304092 A304092(n) = sumdiv(n,d,A102460(d));
%Y A304092 Cf. A000032, A093540, A102460, A304091, A304094, A304096.
%Y A304092 Cf. also A005086, A300837.
%K A304092 nonn
%O A304092 1,2
%A A304092 _Antti Karttunen_, May 13 2018