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A356666
Smallest m such that the m-th Lucas number has exactly n divisors that are also Lucas numbers.
2
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
1,3
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
FORMULA
A000032(a(n)) = A356123(n).
PROG
(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
CROSSREFS
Cf. A105802 (similar for Fibonacci).
Sequence in context: A319643 A092641 A077449 * A152232 A357007 A183038
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 22 2022
EXTENSIONS
a(12)-a(26) from Daniel Suteu, Aug 24 2022
More terms from Daniel Suteu and David A. Corneth, Sep 04 2022
STATUS
approved