A360107 Numbers k such that sigma_2(Fibonacci(k)^2 + 1) == 0 (mod Fibonacci(k)).

1, 2, 3, 5, 7, 9, 11, 13, 15, 19, 21, 25, 27, 31, 41, 45, 49, 81, 85, 129, 133, 135, 139, 357, 361, 429, 431, 433, 435, 447, 451, 507, 511, 567, 569, 571, 573

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Example

7 is in the sequence because the divisors of Fibonacci(7)^2 + 1 = 13^2 + 1 = 170 are {1, 2, 5, 10, 17, 34, 85, 170}, and 1^2 + 2^2 + 5^2 + 10^2 + 17^2 + 34^2 + 85^2 + 170^2 = 37700 = 13*2900 == 0 (mod 13).

Mathematica

Select[Range[140], Divisible[DivisorSigma[2, Fibonacci[#]^2+1], Fibonacci[#]]&]

Prog

(PARI) isok(k) = my(f=fibonacci(k)); sigma(f^2 + 1, 2) % f == 0; \\ Michel Marcus, Jan 26 2023

Crossrefs

Cf. A000045, A001157, A067719, A245236, A245306, A338762, A360105.

Sequence in context: A023543 A129895 A256212 * A096149 A033055 A287374

Adjacent sequences: A360104 A360105 A360106 * A360108 A360109 A360110

Keyword

nonn,more

Author

Michel Lagneau, Jan 26 2023

Extensions

a(24)-a(37) from Daniel Suteu, Jan 27 2023

Status

approved