This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A360105 #19 Apr 04 2024 09:50:16
%S A360105 1,2,5,7,13,25,34,52,89,93,100,200,233,338,610,850,915,1028,1352,1508,
%T A360105 1918,2105,3918,4181,5540,6396,6728,7250,9282,10100,10132,10946,15507,
%U A360105 16609,17125,32708,32776,37107,42568,47770,58218,61230,72125,74948,75025,78608
%N A360105 Numbers k such that sigma_2(k^2 + 1) == 0 (mod k).
%C A360105 Conjecture: the sequence contains infinitely many Fibonacci numbers (see A360107).
%C A360105 For k < 10^7, we observe only 6 prime numbers in the sequence: {2, 5, 7, 13, 89, 233} including the Fibonacci numbers {2, 5, 13, 89, 233} and the Lucas number {7}.
%H A360105 Robert Israel, <a href="/A360105/b360105.txt">Table of n, a(n) for n = 1..222</a>
%e A360105 7 is in the sequence because the divisors of 7^2+1 = 50 are {1, 2, 5, 10, 25, 50}, and 1^2 + 2^2 + 5^2 + 10^2 + 25^2 + 50^2 = 3255 = 7*465 == 0 (mod 7).
%p A360105 filter:= k -> NumberTheory:-SumOfDivisors(k^2+1,2) mod k = 0:
%p A360105 select(filter, [$1..10^5]); # _Robert Israel_, Feb 19 2024
%t A360105 Select[Range[50000], Divisible[DivisorSigma[2, #^2+1], #]&]
%o A360105 (PARI) isok(k) = sigma(k^2 + 1, 2) % k == 0; \\ _Michel Marcus_, Jan 26 2023
%Y A360105 Cf. A000032, A000045, A001157, A067719, A360107.
%K A360105 nonn
%O A360105 1,2
%A A360105 _Michel Lagneau_, Jan 26 2023