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

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

Author

Altug Alkan, Aug 09 2016

Keywords

• nonn

Examples

			a(5) = 12 because Fibonacci(12) = 144 is divisible by sigma(5) = 6.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A001177, A000203, A272412.

Programs

Mathematica

Table[k = 1; While[! Divisible[Fibonacci@k, DivisorSigma[1, n]], k++]; k, {n, 120}] (* Michael De Vlieger, Aug 11 2016 *)

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

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