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Search: id:A105802
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| A105802 |
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Smallest m such that the m-th Fibonacci number has exactly n divisors that are also Fibonacci numbers. |
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+0
3
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| 1, 3, 6, 15, 12, 45, 24, 36, 48, 405, 60, 315, 192, 144, 120, 945, 180, 1575, 240, 576, 3072, 295245, 360, 1296, 12288, 900, 960, 25515, 720, 14175, 840, 9216, 196608, 5184, 1260, 17325, 786432, 36864, 1680, 31185, 2880, 127575, 15360, 3600, 99225
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OFFSET
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1,2
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COMMENT
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A076985(n) = A000045(a(n)); A076984(a(n)) = n.
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LINKS
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Eric Weisstein's World of Mathematics, Fibonacci Number
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FORMULA
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Conjecture: a(2k+1) = 3*2^(Prime[k-1]-1) for k>3. It appears that a(2k+1) = 3*2^k for k = {1,2,3,4,6,10,12,16,18,...} = A068499[n] Numbers n such that n! reduced modulo (n+1) is not zero. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 15 2006
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EXAMPLE
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n=6: a(6) = 45, A076985(6) = A000045(45) = 1134903170,
A076984(45) = #{1,2,5,34,109441,1134903170} = #{fib(1),fib(2),fib(5),fib(9),fib(21),fib(45)} = 6.
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MATHEMATICA
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t=Table[s=DivisorSigma[0, n]; If[OddQ[n], s, s-1], {n, 1000000}]; lst={}; n=1; While[pos=Flatten[Position[t, n, 1, 1]]; Length[pos]>0, AppendTo[lst, pos[[1]]]; n++ ]; lst (Noe)
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CROSSREFS
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Cf. A068499.
Sequence in context: A162276 A144615 A088698 this_sequence A066904 A059969 A124518
Adjacent sequences: A105799 A105800 A105801 this_sequence A105803 A105804 A105805
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 20 2005
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 18 2006
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