A276811 a(n) = sigma(Fibonacci(k))/Fibonacci(n) where k is the least number such that Fibonacci(n) divides sigma(Fibonacci(k)), or -1 if no such k exists.

1, 1, 2, 1, 3, 4, 31, 20, 47, 5832, 322, 84, 4576568315415066934826490, 324, 843, 480, 3769607182320, 2209, 707932145558030519866865515025923563263974776037874477588352, 69670959389872974262939756520, 39603

Offset

1,3

Comments

Least k such that Fibonacci(n) divides sigma(Fibonacci(k)) are 1, 1, 4, 3, 6, 8, 12, 14, 17, 27, 23, 20, 131, 26, 29, 28, 77, 34, 305, 158, 43, ...

Links

Table of n, a(n) for n=1..21.

Example

a(7) = 31 because least k such that Fibonacci(7) divides sigma(Fibonacci(k)) is 12 and sigma(Fibonacci(12))/Fibonacci(7) = 31.

Mathematica

f[n_] := Block[{k = 1, fn = Fibonacci@ n}, While[ds = DivisorSigma[1, Fibonacci[k]]; Mod[ds, fn] > 0, k++]; ds/fn]; Array[f, 21] (* Robert G. Wilson v, Nov 06 2016 *)

Crossrefs

Cf. A000045, A063477, A277261.

Sequence in context: A099866 A365228 A370550 * A317750 A188732 A085189

Adjacent sequences: A276808 A276809 A276810 * A276812 A276813 A276814

Keyword

nonn

Author

Altug Alkan, Nov 05 2016

Status

approved