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

1, 0, 3, 6, 15, 30, 45, 90, 105, 210, 405, 810, 315, 630, 3645, 2025, 945, 1890, 1575, 3150, 2835, 5670, 36450, 25025, 3465, 6930, 101250, 11025, 22050, 51030, 14175, 28350, 10395, 20790, 2952450, 175175, 17325, 34650, 1937102445, 625625, 31185, 62370, 127575, 255150

Offset: 1

Author

Michel Marcus, Aug 22 2022

Keywords

• nonn

Comments

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

Links

• David A. Corneth, Table of n, a(n) for n = 1..382

Crossrefs

Cf. A000032, A038547, A102460, A304092, A356123.

Cf. A105802 (similar for Fibonacci).

Programs

PARI

L(n)=fibonacci(n+1)+fibonacci(n-1); \\ A000032
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
nbld(n) = sumdiv(n, d, isld(d)); \\ A304092
a(n) = my(k=0); while(nbld(L(k)) != n, k++); k;

PARI

countLd(n) = my(c=0,x=2,y=1); while(x<=n, if(n%x==0, c++); [x,y]=[y,x+y]); c;
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

Formula

A000032(a(n)) = A356123(n).

Extensions

a(12)-a(26) from Daniel Suteu, Aug 24 2022

More terms from Daniel Suteu and David A. Corneth, Sep 04 2022