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A275789 Least k such that sigma(n) divides Fibonacci(k) (k > 0).

%I A275789 #24 Aug 16 2016 09:11:21
%S A275789 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,
%T A275789 24,30,24,60,12,24,24,12,36,12,56,18,60,24,60,24,24,30,24,84,12,12,30,
%U A275789 36,60,12,168,36,60,12,60,60,60,60,24,30,24,42,128,24,12,18,24,24,12,12
%N A275789 Least k such that sigma(n) divides Fibonacci(k) (k > 0).
%H A275789 Chai Wah Wu, <a href="/A275789/b275789.txt">Table of n, a(n) for n = 1..10000</a>
%F A275789 a(n) = A001177(A000203(n)). - _Robert Israel_, Aug 09 2016
%F A275789 log n << a(n) << n log log n. - _Charles R Greathouse IV_, Aug 12 2016
%e A275789 a(5) = 12 because Fibonacci(12) = 144 is divisible by sigma(5) = 6.
%t A275789 Table[k = 1; While[! Divisible[Fibonacci@k, DivisorSigma[1, n]], k++]; k, {n, 120}] (* _Michael De Vlieger_, Aug 11 2016 *)
%o A275789 (PARI) a(n)=my(k=1); while(fibonacci(k) % sigma(n), k++); k;
%o A275789 (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
%o A275789 (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
%Y A275789 Cf. A000045, A001177, A000203, A272412.
%K A275789 nonn
%O A275789 1,2
%A A275789 _Altug Alkan_, Aug 09 2016