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A262341
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Largest primitive prime factor of Fibonacci number F(n), or 1 if no primitive.
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1
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1, 1, 2, 3, 5, 1, 13, 7, 17, 11, 89, 1, 233, 29, 61, 47, 1597, 19, 113, 41, 421, 199, 28657, 23, 3001, 521, 109, 281, 514229, 31, 2417, 2207, 19801, 3571, 141961, 107, 2221, 9349, 135721, 2161, 59369, 211, 433494437, 307, 109441, 461, 2971215073, 1103, 6168709, 151
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OFFSET
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1,3
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COMMENTS
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Carmichael proved that a(n) > 1 if n > 12.
See A001578 (smallest primitive prime factor of F(n)) and A061446 (primitive part of F(n)) for more links.
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LINKS
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EXAMPLE
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The prime factors of F(46)= 139 * 461 * 28657 that do not divide any smaller Fibonacci number are 139 and 461, so a(46) = 461.
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MATHEMATICA
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prms={}; Table[f=First/@FactorInteger[Fibonacci[n]]; p=Complement[f, prms]; prms=Join[prms, p]; If[p=={}, 1, Last[p]], {n, 50}]
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PROG
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(Perl) use ntheory ":all"; my %s; for (1..100) { my @f = factor(lucasu(1, -1, $_)); pop @f while @f && $s{$f[-1]}++; say "$_ ", $f[-1] || 1; } # Dana Jacobsen, Oct 13 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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