A356122 Number of Lucas divisors of the n-th Lucas number.

2, 1, 2, 3, 2, 2, 4, 2, 2, 4, 3, 2, 4, 2, 3, 5, 2, 2, 5, 2, 3, 5, 3, 2, 4, 3, 3, 5, 3, 2, 6, 2, 2, 5, 3, 4, 5, 2, 3, 5, 3, 2, 6, 2, 3, 7, 3, 2, 4, 3, 4, 5, 3, 2, 6, 4, 3, 5, 3, 2, 6, 2, 3, 7, 2, 4, 6, 2, 3, 5, 5, 2, 5, 2, 3, 7, 3, 4, 6, 2, 3, 6, 3, 2, 6, 4, 3, 5, 3, 2, 8, 4, 3, 5, 3, 4, 4, 2, 4, 7

Offset: 0

Author

Michel Marcus, Jul 27 2022

Keywords

• nonn

Links

• Daniel Suteu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000032, A102460, A304092, A356062, A356123.

Cf. A076984 (similar for Fibonacci numbers).

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) = nbld(L(n));

PARI

a(n) = if(n==1, return(1)); my(k=fibonacci(n+1)+fibonacci(n-1),c=0,x=2,y=1); while(x <= k, if(k%x == 0, c++); [x,y]=[y,x+y]); c; \\ Daniel Suteu, Aug 25 2022

Formula

a(n) = A304092(A000032(n)).