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 A282849 #31 Nov 16 2017 02:53:29
%S A282849 1,2,0,2,0,4,0,0,0,4,0,4,0,0,0,2,0,4,0,0,0,4,0,2,0,0,0,4,0,8,0,0,0,2,
%T A282849 0,4,0,0,0,4,0,8,0,0,0,2,0,2,0,0,0,4,0,2,0,0,0,4,0,8,0,0,0,0,0,4,0,0,
%U A282849 0,8,0,4,0,0,0,2,0,8,0,0,0,4,0,4,0,0,0,4,0,6
%N A282849 Number of divisors k of n such that (n + k^2)/k is a prime.
%C A282849 Except for the single case of a(1)=1 all terms are even. - _Robert G. Wilson v_, Feb 25 2017
%C A282849 First occurrence of 2k: 3, 2, 6, 90, 30, 390, 690, 420, 210, 4290, 3990, 8778, 2310, 3570, 4830, 11550, 38850, 84630, 66990, 79170, 39270, 30030, 51870, 46410, 43890, ..., . - _Robert G. Wilson v_, Feb 25 2017
%H A282849 Robert G. Wilson v, <a href="/A282849/b282849.txt">Table of n, a(n) for n = 1..10000</a>
%H A282849 Michael De Vlieger, <a href="/A282849/a282849.txt">Records and indices of records</a>.
%F A282849 a(1) = 1; for n > 0: a(2n) = 2*A088627(n), a(2n + 1) = 0.
%e A282849 a(6) = 4 because (6 + 1^2)/1 = 7 is prime, (6 + 2^2)/2 = 5 is prime, (6 + 3^2)/3 = 5 is prime, (6 + 6^2)/6 = 7 is prime, where 1, 2, 3 and 6 are divisors of 6.
%t A282849 f[n_] := Block[{d = Divisors@ n}, Length@ Select[d, PrimeQ[(n + #^2)/#] &]]; Array[f, 105] (* _Robert G. Wilson v_, Feb 25 2017 *)
%t A282849 Table[DivisorSum[n, 1 &, PrimeQ[(n + #^2)/#] &], {n, 105}] (* _Michael De Vlieger_, Nov 15 2017 *)
%o A282849 (PARI) a(n) = sumdiv(n, k, isprime((n+k^2)/k)); \\ _Michel Marcus_, Feb 26 2017
%Y A282849 Cf. A088627 (number of divisors k of n such that (n + 2*k^2)/k is prime), A047255.
%K A282849 nonn
%O A282849 1,2
%A A282849 _Juri-Stepan Gerasimov_, Feb 24 2017