A350690 Numbers k that divide the sum of divisors of Fibonacci(k).

1, 3, 4, 7, 8, 9, 13, 14, 16, 17, 18, 19, 21, 23, 24, 26, 27, 28, 30, 31, 32, 34, 36, 37, 38, 39, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 61, 62, 63, 64, 67, 68, 69, 70, 71, 72, 73, 74, 76, 78, 79, 81, 83, 84, 86, 87, 88, 90, 91, 92, 93, 94, 96

Offset

1,2

Comments

This sequence is infinite (Luca, 2002).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1197

Florian Luca, Problem H-590, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 40, No. 5 (2002), p. 472; Arithmetic Functions of Fibonacci Numbers, Solution to Problem H-590 by J.-Ch. Schlage-Puchta and J. Spilker, ibid., Vol. 41, No. 4 (2002), pp. 382-384.

Example

3 is a term since 3 divides sigma(Fibonacci(3)) = sigma(2) = 3.
4 is a term since 4 divides sigma(Fibonacci(4)) = sigma(3) = 4.

Mathematica

Select[Range[100], Divisible[DivisorSigma[1, Fibonacci[#]], #] &]

Prog

(Python) from sympy import divisor_sigma, fibonacci
print([k for k in range(1, 97) if divisor_sigma(fibonacci(k)) % k == 0])
# Karl-Heinz Hofmann, Jan 12 2022

Crossrefs

Cf. A000045, A000203, A063477.

Similar sequences: A074698, A075775.

Sequence in context: A100452 A004201 A109054 * A363751 A129142 A359749

Adjacent sequences: A350687 A350688 A350689 * A350691 A350692 A350693

Keyword

nonn

Author

Amiram Eldar, Jan 12 2022

Status

approved