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A275789
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Least k such that sigma(n) divides Fibonacci(k) (k > 0).
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1
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1, 4, 6, 8, 12, 12, 6, 20, 7, 12, 12, 24, 24, 12, 12, 30, 12, 28, 30, 24, 24, 12, 12, 60, 30, 24, 30, 24, 60, 12, 24, 24, 12, 36, 12, 56, 18, 60, 24, 60, 24, 24, 30, 24, 84, 12, 12, 30, 36, 60, 12, 168, 36, 60, 12, 60, 60, 60, 60, 24, 30, 24, 42, 128, 24, 12, 18, 24, 24, 12, 12
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 12 because Fibonacci(12) = 144 is divisible by sigma(5) = 6.
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MATHEMATICA
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Table[k = 1; While[! Divisible[Fibonacci@k, DivisorSigma[1, n]], k++]; k, {n, 120}] (* Michael De Vlieger, Aug 11 2016 *)
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PROG
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(PARI) a(n)=my(k=1); while(fibonacci(k) % sigma(n), k++); k;
(PARI) a(n)=my(s=sigma(n), a=Mod(1, s), b=a, k=1); while(a, [a, b]=[b, a+b]; k++); k \\ Charles R Greathouse IV, Aug 12 2016
(Perl) use ntheory ":all"; sub a275789 { my($sigma, $k)=(divisor_sum(shift), 1); return 1 if $sigma==1; $k++ while (lucas_sequence($sigma, 1, -1, $k))[0]; $k; } # Dana Jacobsen, Aug 15 2016
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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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