A356123 -id:A356123 - cp's OEIS frontend

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

Michel Marcus, Jul 27 2022

nonn

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

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

Cf. A076984 (similar for Fibonacci numbers).

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));

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

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

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

Original entry on oeis.org

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

Michel Marcus, Aug 22 2022

nonn

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

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

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

Cf. A105802 (similar for Fibonacci).

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;

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

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

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

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

cp's OEIS Frontend

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

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

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