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A356666 Smallest m such that the m-th Lucas number has exactly n divisors that are also Lucas numbers.

%I A356666 #19 Sep 04 2022 12:35:44
%S A356666 1,0,3,6,15,30,45,90,105,210,405,810,315,630,3645,2025,945,1890,1575,
%T A356666 3150,2835,5670,36450,25025,3465,6930,101250,11025,22050,51030,14175,
%U A356666 28350,10395,20790,2952450,175175,17325,34650,1937102445,625625,31185,62370,127575,255150
%N A356666 Smallest m such that the m-th Lucas number has exactly n divisors that are also Lucas numbers.
%C A356666 Further terms <= 51030: a(28) = 11025, a(29) = 22050, a(30) = 51030, a(31) = 14175, a(32) = 28350, a(33) = 10395, a(34) = 20790, a(37) = 17325, a(38) = 34650, a(41) = 31185, a(49) = 45045. - _Daniel Suteu_, Aug 24 2022
%H A356666 David A. Corneth, <a href="/A356666/b356666.txt">Table of n, a(n) for n = 1..382</a>
%F A356666 A000032(a(n)) = A356123(n).
%o A356666 (PARI) L(n)=fibonacci(n+1)+fibonacci(n-1); \\ A000032
%o A356666 isld(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)); }; \\ A102460
%o A356666 nbld(n) = sumdiv(n, d, isld(d)); \\ A304092
%o A356666 a(n) = my(k=0); while(nbld(L(k)) != n, k++); k;
%o A356666 (PARI)
%o A356666 countLd(n) = my(c=0,x=2,y=1); while(x<=n, if(n%x==0, c++); [x,y]=[y,x+y]); c;
%o A356666 a(n) = if(n==1, return(1)); my(k=0,x=2,y=1); while(1, if(countLd(x) == n, return(k)); [x,y,k]=[y,x+y,k+1]); \\ _Daniel Suteu_, Aug 24 2022
%Y A356666 Cf. A000032, A038547, A102460, A304092, A356123.
%Y A356666 Cf. A105802 (similar for Fibonacci).
%K A356666 nonn
%O A356666 1,3
%A A356666 _Michel Marcus_, Aug 22 2022
%E A356666 a(12)-a(26) from _Daniel Suteu_, Aug 24 2022
%E A356666 More terms from _Daniel Suteu_ and _David A. Corneth_, Sep 04 2022