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Search: id:A016089
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| A016089 |
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Numbers n such that n divides n-th Lucas number A000032(n). |
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4
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| 1, 6, 18, 54, 162, 486, 1458, 1926, 4374, 5778, 13122, 17334, 39366, 52002, 118098, 156006, 206082, 354294, 468018, 618246, 1062882, 1404054, 1854738, 2471058, 3188646, 4212162, 5564214, 7413174, 9565938, 12636486, 16692642, 22050774
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OFFSET
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1,2
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COMMENT
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Note that if n divides A000032(n) and p is an odd prime divisor of A000032(n), then pn divides A000032(pn) and, furthermore, p^k*n divides A000032(p^k*n) for every integer k>=0.
In particular, since 6 divides A000032(6) = 2*3^2, A016089 includes all terms of the geometric progression 2*3^k for k>0 (see A099856); since 18 divides A000032(18) = 2*3^3*107, A016089 includes all terms of the form 2*107^m*3^k for k>1 and m>=0; etc.
Terms of A016089 starting with 18 are multiples of 18. There are no other terms of the form 18p where p is prime, except for p=3 and p=107. - Alexander Adamchuk (alex(AT)kolmogorov.com), May 11 2007
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MATHEMATICA
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a = 1; b = 3; Do[c = a + b; a = b; b = c; If[Mod[c, n] == 0, Print[n]], {n, 3, 2, 10^6}]
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CROSSREFS
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Cf. A000032, A000204, A025192, A008776.
Cf. A099856, A072378 = numbers n such that 12n divides Fibonacci(12n), A023172 = numbers n such that n divides Fibonacci(n).
Sequence in context: A006779 A003208 A002933 this_sequence A099856 A007206 A056349
Adjacent sequences: A016086 A016087 A016088 this_sequence A016090 A016091 A016092
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Extended and revised by Max Alekseyev, May 13 2007, May 15 2008, May 16 2008
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