

A065156


Numbers n such that some Lucas number (A000204) is divisible by n.


4



1, 2, 3, 4, 6, 7, 9, 11, 14, 18, 19, 22, 23, 27, 29, 31, 38, 41, 43, 44, 46, 47, 49, 54, 58, 59, 62, 67, 71, 76, 79, 81, 82, 83, 86, 94, 98, 101, 103, 107, 116, 118, 121, 123, 124, 127, 129, 131, 134, 139, 142, 151, 158, 161, 162, 163, 166, 167, 179, 181, 191, 199
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OFFSET

1,2


COMMENTS

For the Fibonacci numbers, each natural number divides some Fibonacci number (see A001177).
If, for some number m, m divides some Lucas number L_i (=A000204(i)), then, the smallest i satisfies i <= m. (End)


LINKS



FORMULA



MATHEMATICA

test[ n_ ] := For[ a=1; b=3, True, t=b; b=Mod[ a+b, n ]; a=t, If[ b==0, Return[ True ] ]; If[ a==2&&b==1, Return[ False ] ] ]; Select[ Range[ 200 ], test ]
Take[Flatten[Divisors/@LucasL[Range[200]]]//Union, 70] (* Harvey P. Dale, Jun 07 2020 *)


PROG

(Python)
a, n = 0, 0
while n < 1000:
a, f0, f1, i = a+1, 1, 2, 1
if f1%a == 0:
n = n+1
print(n, a)
else:
while f0%a != 0 and i <= a:
f0, f1, i = f0+f1, f0, i+1
if i <= a:
n = n+1


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



