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A275789
Least k such that sigma(n) divides Fibonacci(k) (k > 0).
1
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
OFFSET
1,2
FORMULA
a(n) = A001177(A000203(n)). - Robert Israel, Aug 09 2016
log n << a(n) << n log log n. - Charles R Greathouse IV, Aug 12 2016
EXAMPLE
a(5) = 12 because Fibonacci(12) = 144 is divisible by sigma(5) = 6.
MATHEMATICA
Table[k = 1; While[! Divisible[Fibonacci@k, DivisorSigma[1, n]], k++]; k, {n, 120}] (* Michael De Vlieger, Aug 11 2016 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Aug 09 2016
STATUS
approved