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
Keywords
Examples
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.
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.
Programs
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Mathematica
Select[Range[100], Divisible[DivisorSigma[1, Fibonacci[#]], #] &]
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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
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